Frobenius morphisms and stable module categories of repetitive algebras

Let k be the algebraic closure of a finite field F-q and A be a finite dimensional k-algebra with a Frobenius morphism F. In the present paper we establish a relation between the stable module category of the repetitive algebra (A) over cap of A and that of the repetitive algebra of the fixed-point algebra A(F). As an application, it is shown that the derived category of A(F) is equivalent to the subcategory of F-stable objects in the derived category of A when A has a finite global dimension.