The police haven’t yet said anything about the identity of the Manchester suicide bomber, but the Islamic State has claimed responsibility. Here's the statement.
This is the same layout as the statement released
on social media after the Bataclan attacks, complete with the bizarre “breaking news” box on the top left and references to the murdered young girls as “crusaders”. Its death toll is wrong – 22 are understood to have died, not 30. But it does suggest that the targeting of a pop concert attended by girls and their parents was deliberate, referring to the show as “shameless.” It had similar things to say about the Bataclan concert (a "profligate prostitution party") and it also then threatened worse attacks to come.
Can we believe the Isil statement? That's still unclear. The statement took some time to appear. Pro-Islamic State social media has been celebrating the Manchester attack since it happened: see below from SITE intelligence, which monitors such things). US officials say that it looks fishy, and that Isil might be claiming credit for an attack that it inspired rather than directed.