May 22, 2012 03:00 PM

When they embark on their upcoming European summer tour, The All-American Rejects will be without one of their unofficial members: guitarist Nick Wheeler’s dog, Dexter.

“He’s become part of the family,” Wheeler tells PEOPLE. “I think everybody would agree that when he’s not around, it’s not going to be the same.”

Dexter, a 4-year-old Boston terrier mix, has been traveling with the rock band since Wheeler adopted him in late 2009. To Wheeler’s surprise – and subsequent joy – Dexter easily adapted to life on the road.

“He’s a tour machine,” Wheeler says. “He loves it, everybody loves him, he gets along with everybody, so now he goes along everywhere.”

Dexter’s past life as a stray and a shelter dog was part of the inspiration for the band’s new partnership with Petfinder, for which they’ve already given away concert tickets and signed albums. (Keep an eye on Petfinder’s Facebook page for updates.)

“I’m in a position with my band, and now with Petfinder, to promote pet adoption, which I believe is the right way to go,” Wheeler says. “The stuff you see on TV [about adoption] is so depressing. For me, it’s not about that. For me, this is my best friend. I wanted to put a positive spin on things.”

Wheeler’s best friend has already changed the dynamic between The All-American Rejects and their fans, who have taken a liking to the band’s “unofficial fifth member.”

“Everybody wants to meet Dexter, more than they want to meet us sometimes,” Wheeler says. “He had met so many people, that near the end of the last tour, he would go to meet-and-greets after shows, and just hide under the table. ‘I’m over it! I’m tired of all these people!’”

Luckily, Dexter’s been able to catch a break from the frenzy of traveling and dealing with his groupies, and has been hanging out at Wheeler’s Los Angeles home.

“We were both really excited to get back to my California king-sized Tempurpedic bed,” Wheeler says. “He makes a little palace out of my pillows and chills there all day long.”

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