Kanojo wa Uso wo Aishisugiteru

From Nagareboshi Manga & Manga Abyss: Ogasawara Aki is the reclusive, idealistic composer of the popular band Crude Play. Discontented with his life and with no drive to succeed, he meets Riko, the 16-year-old grocer's daughter in a band consisting of her childhood friends, and asks her to be his girlfriend on a whim. Riko, young and innocent, agrees immediately, but worries about her new boyfriend, whom she suspects has just broken up with a woman he cared very much for.