For the last decade, Interpol has been one of the darlings of the independent music scene. Their seminal first album, “Turn On The Bright Lights,” was released in 2002 to massive critical acclaim. Nearly ten years later, they’re still going strong. Interpol is famous as a New York City band, but part of their roots are right here in Ohio. Their very first U.S. tour began in Cleveland, at a little spot called the Grog Shop. Ever since, they’ve made a point of stopping in Ohio when they can. “We always have good shows in Ohio,” said Daniel Kessler, guitarist, vocalist and founding member. From the beginning, Interpol was all about making good music, not just music other people wanted to make. They formed because Kessler “really wanted to form a band,” he said. “Clear art influences were never that important to me.” This idealism is what gives Interpol their distinctive sound — one that Kessler is hesitant to classify. “The only thing I ever dreamed of was making a record with a respected record label,” he said. “We’re just a rock and roll band. It’s not up to me to define. It’s up to other people to philosophize as to what we are.” In his search for musicians, he recruited Paul Banks (vocals, guitar), Carlos Dengler (bass, keys) and Greg Drudy (drums), and Interpol was formed. Drudy left in 2000 and was replaced by Sam Fogarino, who has been with them ever since. They plied their trade for five years before releasing their first LP in 2002, and have slowly risen to fame since. Now, they’re touring with U2, headlining festivals and promoting their newest album “Interpol” with a tour of their own. Returning to their indie roots, the eponymous album is part of their move away from major-label involvement with Columbia, back to their home on Matador. The release of the album unfortunately also heralded the release of Dengler, who left amicably to pursue other projects. Thanks to Interpol’s reputation, there’s a long list of bassists waiting to fill his shoes for the tour while they decide on a permanent replacement. When Interpol comes to Cleveland, they’ll be headlining their own show — something they’re looking forward to after months of opening. U2’s fans “were very kind to us and very receptive,” said Kessler, but they’re ready to get on stage in front of strictly Interpol fans. Interpol will be appearing July 18 at the House of Blues in Cleveland. Tickets range from $29.50 to $37.50; show starts at 7 p.m.