In this tangled Finnish crime saga, nearly everyone is either undercover, using an alias, not in the job they claim to be doing, or pretending to be someone else. No wonder a weary cop claims, quite some way into the narrative: “We don’t really know what we’re investigating.”

A young woman is shot by a drug dealer at Helsinki airport, but the police who arrive on the scene acting on “an anonymous tip” have no idea who she is, and some mysterious entity spirits the body away from the morgue. They take in her surly companion, but before the weary but shrewd investigator Timo Viita (Tommi Korpela) can prise out any information, a message comes from on high that she must be released. “Who is this woman?” becomes the series’ mantra. This one officially goes by the name Mari Saari, except we already know she’s been assigned it, plus a new identity, a cover story and a flat, by a striking older woman (Outi Mäenpää) she met on a park bench.

Then there’s the nervous Afghan lady in a headscarf who turns up at the airport claiming political asylum, with a false passport in the name of Zamira Hoxha. Her real name seems to be Madina Taburova, but I wouldn’t believe anything at this point. The criminals, too, are operating on different layers of reality, where a counterfeiting operation morphs into people-trafficking, which is a cover for drug smuggling, except that the real booty is ammo, sneaked into Europe from the Middle East via the flow of migrants. Some viewers will be thanking God we’re not in the EU by this stage.

The substitutions and impersonations continue to accumulate. Just as Madina (Sibel Kekilli) has taken over the life of the unfortunate Zamira, so Mari (Krista Kosonen), in one of the rare moments she allows herself to feel emotion, reflects on the fate of her colleague: “That bullet was meant for me.” The dealer, Jari Holma (Juho Milonoff), presents another puzzle. When one more body is found, the cops debate whether he could be the killer. “Maybe.” “I’d say probably.” Only Timo frets that it's not Holma’s usual MO. It's a concept he might as well jettison in this topsy-turvy world.

Some flashback business in a dusty mountain pass in Afghanistan gives a chilling resonance to the title. “I don’t want to be a bullet,” mutters yet another mystery woman. What’s her story? A long, brooding silence is the only response. It’s enough to make you dizzy; but I reckon plodding Timo will eventually get to the bottom of it.

★★★★☆

Available on All4 now

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