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Poor Martin McDonagh. Once regarded as a flashy Irish wunderkind with the rawest of talents and now an established London playwright with a following and attitude to match, he has always been a rootless enigma.

McDonagh’s theatrical fame flowed from chronicling the trapped locals of Connemara and Inishmaan, yet McDonagh himself is a freewheeling child of the Irish Diaspora who grew up in London. In cities such as Chicago or New York, he still gets claimed by actors hungry for authentic Irish poetry as a legitimate heir to J.M. Synge or Brian Friel, yet he actually has been more influenced by the post-modern American rhythms of David Mamet or Sam Shepard.

And here in Britain, where the pervasive mode of playwriting is talky and political and socially committed, the snooty rap against McDonagh long has been that such commercially successful plays as “The Lonesome West” are quite stylish, exciting and flashy, thank you very much, but they don’t really have anything useful to say about anything serious.

All of this appears to have messed up the fellow. But he’s a dangerously prodigious master of theatrical form with a talent that goes far deeper than most people understand. The attacks were good for him. In “The Pillowman,” McDonagh’s thoroughly startling and genuinely intimidating new play at the National Theatre’s Cottesloe Theatre, he effects a rather spectacular kind of theatrical revenge.

“Pillowman” has nothing to do with Ireland and everything to do with McDonagh’s own self-image as a writer.

Set in an unnamed totalitarian state, most of the play takes place in a police interrogation room where a terrified writer improbably named Katurian Katurian (David Tennant) is being interrogated for murder by an intentionally iconic good cop (Jim Broadbent of “Moulin Rouge” fame) and a bad cop (Nigel Lindsay). The officers owe their identity to a weird blend of Harold Pinter and Starsky and Hutch.

It seems that Katurian has been writing gruesome stories that involve the horrible torture and murder of children — such delights as a father who sticks razor blades in his daughter’s apples or parents who crucify and then bury alive their 8-year-old girl.

At first we think the writer has been arrested for reasons of censorship. But we quickly realize that real murder has been involved — seemingly sparked by these stories.

And then the stories — and we’re talking fully staged Grand Guignol vignettes replete with blood, corpses, dead children and piercing sound effects — take over the play. Before intermission, large sections of the theater were emitting screams every few minutes.

When this dark and gory story lands on Broadway (as it surely will), it’s likely to be a big commercial hit, especially if John Crowley’s cynically funny and savvy production goes along for the ride.

Tennant effects a rather strange neutrality, but Broadbent alone is worth the price of admission. His warm and fruity northern English accent offers an intensely ironic counterpoint to a character inclined to torture and shooting people in the head. And bad cop Lindsay somehow manages to be simultaneously vulnerable and the stuff of nightmares.