The 23-year-old formerly known as Stefani Germanotta must be pop's most ruthlessly effective self-promoter since Madonna. In the last few days alone, headlines about her have read "Lady Gaga Bares All (As Usual)"; "Lady Gaga spits fire from her breasts" or, as one paper said, " … sets her boobs on fire."

And yet not all publicity is good publicity. Gaga's failure to show up for scheduled shows with Take That in this city on Saturday and Sunday left 100,000 booing fans and an angry Gary Barlow. Still, forgiven by her own Mancunian fans, she arrives tonight in a blaze of roars and mobile phone cameras – opening, ironically enough, with Paparazzi, a song about being stalked by the camera's eye. This is the level of fame Gaga has planned for, and it looks like she will get it. "Make me a star, Man-che-star!" she wails.

With her debut The Fame making its home in the top five, there are already Gaga lookalikes in an audience of mainly young females hanging on every word. Some of those words – about "the kids shooting the paparazzi", and the mock Warhol movies between songs – go over the audience's heads. She's on safer ground asking, "Do you think you're sexy?" or squealing "Man-che-star!".

Flitting between a racy black bra to a dress apparently made of glass, Gaga is a pop cyborg, a robot Debbie Harry/Edie Sedgewick creation with a voice the size of China. She has two default modes. Like the early Material Girl, she sells aspiration – songs address being "beautiful, dirty and rich" and claim "it's good to live expensive", a factual statement from a girl who went to the same school as Paris Hilton.

And she sells sex. When she compares Manchester to "a good fuck" and waggles a seemingly naked bottom, you fear for the souls of the younger children in the crowd. Like Madonna, she reveals everything but actually tells us nothing. But she's savvy enough to know she'll need more for a career as long as Madge's, and love songs like Brown Eyes (delivered at a glass piano) suggest there is more in the armoury of this classically trained musician.

At an hour with no encore, the show feels flimsy, but it's hard to argue with pop hits like Poker Face and Just Dance. There are chants of "Gaga" long after flames spray from her nipples, which presumably means "Lady Gaga set Manchester on fire".

At Wembley Stadium, London (supporting Take That), until Sunday. Box office: 0844 980 8001.