Abstract: In this talk we give a geometric interpretation of characters of certain representations of p-adic GL(n), which are usually called depth zero supercuspidal representations, in terms of Euler characteristics of certain character sheaves. Our work relies on Lusztig's theory of character sheaves, and in some sense suggests a general framework for relating character sheaves on groups over a nonarchimedean local field to smooth representations. (Joint with Clifton Cunningham.)