Like David Bowie, Peter Gabriel has never had problems shedding his skin. He’s transitioned over the years from art-rock character actor to artful solo performer, world-music explorer, funkmeister, activist, and Hollywood crooner.

Fans who first embraced the singer/songwriter/keyboardist’s music decades ago, when he was frontman for the legendary English progressive-rock band Genesis, may have been shocked when he appeared on the 1999 Grammy broadcast crooning Randy Newman’s "That’ll Do," from the Babe: Pig in the City (Geffen) soundtrack. But if anything, his history has prepared them for the unpredictable. So it wasn’t surprising to find Gabriel — now 53, gray-bearded, and a bit portly — rolling around the Tweeter Center stage in a giant hamster ball a week ago Thursday. Or to hear him take a moment to compare America’s current imperialist ways with those of the now-fallen British Empire, adding that "we are never free until we learn to respect the rights of others." Or to close his set, as he often has in the past, with "Biko," his stirring, tribal-beat tribute to the South African journalist Stephen Biko, who was killed by police while fighting apartheid.

The one constant in Gabriel’s career has been quality. He’s a thoughtful lyricist, a performer with a taste for colorful staging, and a musician whose imagination seems to know few bounds. He also chooses his company wisely. The songs on his most recent album, Up (Geffen), are among his thorniest and most introspective, dealing with the psychic demons of childhood and maturity and the problem of finding one’s humanity in a world turning inhumane. And their music is full of twisty details that make them some of modern pop’s most sonically arresting works. But his seven-piece line-up — which includes his daughter Melanie singing, long-time guitarist David Rhodes, and the remarkable bassist Tony Levin — made easy work of numbers like the sizzling electronic firestorm "Signal to Noise" as well as the graceful, Anne Sexton–inspired "Mercy Street," for which Gabriel and his players moved to the front of the stage and joined their voices in its a cappella introduction.

Older hits, like his breakthroughs "Solsbury Hill," "Shock the Monkey," and "Sledgehammer," were pleasing, but the show’s two new, unrecorded numbers, one of them the cautionary tale of isolationism "The Tower That Ate People," reflected Gabriel’s current interest in bristling, gnarled compositions. His fondness for cultural exploration was also in evidence, in the often microtonal melodic turns and elaborate rhythmic structures of his music and in his choice of the energetic, powerful Uzbekistani singer Sevara and her folk-rock band as the evening’s opening act.