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

Let Λ be an arbitrary monomial algebra. We investigate the stable category GprojZΛ of graded Gorenstein-projective Λ-modules and the orbit category GprojZ Λ/(1) induced by GprojZΛ and the degree shift functor $(1)$. We prove that GprojZΛ is triangle equivalent to the bounded derived category of a path algebra of Dynkin type A and that GprojZΛ/(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 Λ-modules.