Will Keen embodies Russia’s president in a West End production. “It’s been fascinating how the perception of him and the play keep changing,” he said.On a recent evening, the British actor Will Keen was onstage at the Noël Coward Theater in London playing one of the world’s most divisive men: President Vladimir V. Putin of Russia.For much of the first half of “Patriots,” which is largely set in the 1990s after the Soviet Union’s collapse, Keen portrays the character sympathetically — as a minor politician who could only afford cheap suits and whose success was dependent on a friend’s largess. Later on, when an adviser suggests Putin, now president, should keep his enemies close, Keen’s portrayal becomes chilling. “Why would I want to do that,” he replies, “when I can simply destroy them?”Written by Peter Morgan, the creator of “The Crown,” “Patriots” stars Tom Hollander as Boris Berezovsky, a real-life oligarch who made a fortune in post-Soviet Russia, only to fall out with Putin and end up exiled in London, where he died under mysterious circumstances, in 2013.Despite that focus, it’s Keen’s performance that has grabbed attention since the play debuted at the Almeida Theater, in London, last June. Arifa Akbar, in The Guardian, said that even when Putin “grows more megalomaniacal, Keen avoids caricature and keeps his character’s self-righteous desire for Russian imperialism convincingly real, and chilling.” Matt Wolf, reviewing that production for The New York Times, said that Keen “astonishes throughout.” In April, Keen won the best supporting actor award at the Olivier Awards, Britain’s equivalent of the Tonys.In a recent interview at the Noël Coward theater, where “Patriots” is running through Aug. 19, Keen said that, although the script was written long before Russia’s invasion of Ukraine in 2022, the war had changed the feel of the play, making it seem as much Putin’s “origin story” as the tale of an oligarch’s demise. Keen, 53, said that his performance made some audiences uneasy, but it was “nice to be in a show that’s asking questions, rather than providing answers.”In an interview, Keen discussed what he’d learned by getting inside Putin’s head. The following are edited excerpts from that conversation.Keen, right, and Tom Hollander, who plays Boris Berezovsky, an oligarch who died in London under mysterious circumstances in 2013. Marc BrennerWhy did you want to play such a figure?Well, I first learned about it in 2021 — so before the invasion. It didn’t feel as present as it does now. He felt like an autocratic and terrifying figure, obviously, but he didn’t feel like an autocratic and terrifying figure who was also impinging on the world’s safety. It’s been fascinating how the perception of him and the play keep changing.You’re often played villains or antiheroes, including Macbeth and Father MacPhail in “His Dark Materials.” Do you worry about being typecast?As a citizen, I might look at these people as villains, but as an actor, I can’t do that. I want to be as sympathetic as possible to the character — or as empathetic, at least. Putin is a baddie, but I don’t want to be playing him as a pantomime.I’m really interested by our perception of autocrats. From our side, it’s an image of immorality. But in order to do the things that he’s done, he must have an incredibly intense sensation of his own morality — an idea of justice, an idea that he’s setting wrongs right.Some political commentators say Putin is motivated by a desire to restore the Soviet Union. Is that what you mean by setting wrongs right?I’m not in any position to comment politically, but my sense of the character is of somebody who has a particularly deeply sensitized attitude to betrayal. It’s a bit like the medieval idea of kingship, where the king becomes the country in some way: There’s this sense in which Russia — the land — is his body and there’s an absolutely personal, almost physical betrayal, in the break up of the union.What Peter Morgan does so brilliantly in the play is show how Putin’s personal friendships, and the betrayals he experiences in them, impinge on the political sphere too.Theater critics have praised you for mimicking Putin physically, as much as the emotion of the performance. How did you prepare for this?Well, I read and read and read and watched and watched and watched.Physically, what was most useful to me was just observing him in press conferences — I got this enormous sense of inner turmoil, covered by an incredible physical stillness. There’s a sense of containment to him, like he’s trying to hold everything inside.A lot of people have noticed that stillness, especially of the right hand not moving in his walk. And there are other ex-K.G.B. people who have the same thing. The K.G.B. also talk about channeling your tension into your foot. And you do observe his right foot moving very slowly in interviews under the table. Onstage, I also find that tension in him coming out in my fingers.As a citizen, I might look at these people as villains, but as an actor, I can’t do that,” Keen said. “I want to be as sympathetic as possible to the character.”Marc BrennerAs the invasion unfurled, did you change anything in your portrayal?Of course you think about the conflict, but we didn’t discuss, “Let’s make him more chilling” or anything like that. The way the play’s written, it’d be chilling whenever it was performed.I think it’s actually dangerous to think about the effect you’ll have on audience. All you can think about really is, “Is it true?”This isn’t the only recent play in London featuring Putin. In 2019, Lucy Prebble had a hit with “A Very Expensive Poison” about his involvement in the murder of Alexander Litvinenko, a spy-turned-whistle-blower. Why do you think Putin is becoming a staple of British theater?Well, I don’t know whether he’s becoming a staple. But it does seem that what has happened in Russia lends itself to extremely interesting plays — this ideological battle that’s going on with incredibly high stakes.And theater since time immemorial has studied autocrats, and strong and violent authority is a productive, dramatic force against which to set any kind of dissident opinion.All the characters that one has played sort of talk to each other, at some level, but I would compare Putin to Macbeth, of course. They’re obvious autocrats, but for Macbeth the great motivator is fear, whereas, here, I’d say it’s perceived injustice. The result in both cases is a sort of very performed manliness.What have audience reactions been like?Absolutely wonderful, although sometimes it does seem people don’t know what to do at the end: Should we clap? A lot of Russians have said they feel like he’s in the room, which is incredibly encouraging.I don’t think I’ve spoken to any Ukrainians about it. I’ve had boos, definitely, at the end. But I don’t know whether that was a Ukrainian boo or a British boo. There’s a kind of international language of booing.Has the role affected you personally?No, I wash him off at the end of the show. But it is a bleak place to inhabit — not because of a sense of guilt, it’s the agony of being someone who is obsessed by betrayal and vengeance. More