The stable category of Gorenstein-projective modules over a monomial algebra

Let be an arbitrary monomial algebra. We investigate the stable category Gproj^Z of graded Gorenstein-projective -modules and the orbit category Gproj^Z / (1) induced by Gproj^Z and the degree shift functor (1). We prove that Gproj^Z is triangle equivalent to the bounded derived category of a path algebra of Dynkin type A and that Gproj^Z/ (1) is triangle equivalent to the stable module category of a self-injective Nakayama algebra. Both the path algebra and the self-injective Nakayama algebra will be given explicitly. The latter result provides an explicit description of the stable category of (ungraded) Gorenstein-projective -modules.