By Kevin O'Donnell
April 30, 2012 12:00 PM

For most musicians, there’s nothing bigger than becoming a member of the Rock and Roll Hall of Fame. Axl Rose has another opinion. After years of feuding with his former bandmates, the singer not only opted out of attending the April 14 ceremony in Cleveland where Guns N’ Roses was to receive the honor, but he said in an open letter, “I respectfully decline my induction.” His alternate plans? The night before the event a source told PEOPLE, “He has every intention of enjoying the California weather.”

The headline-making dis wasn’t a surprising move for the rocker, 50, who has become increasingly more known for his looks and his behavior than for his music. Sporting cornrows and a taut face at the 2002 MTV Video Music Awards! A brawl with Tommy Hilfiger in ’06! And yet, after selling nearly 20 million records, he remains a beloved-if elusive (he rarely gives interviews)-pop icon. In fact, at a pre-Golden Globes bash in January, Madonna, Steven Tyler and other guests sought out Rose. “There were all these movie stars, and he was the only person anyone wanted to see,” says an observer. The singer likes life out of the spotlight-yet he still lives like a rock star. “He stays up all night playing music … [and] doesn’t get up until well into the afternoon,” an industry pal says of Rose’s routine. Says a music source: “He enjoys the good life-nice cars and expensive jewelry.” Not to mention bowling, exotic animals and fiddling with electronics (see box).

Music, however, is still his priority. Rose’s recent Guns N’ Roses shows (he’s the only original member) have earned raves, and his band kicks off a European tour in May. So what if he doesn’t take the stage until after midnight? As his latest behavior proves, “he’s Axl,” says pal Sharon Osbourne. “He can do what he wants.”