Realizing stable categories as derived categories

In this paper, we discuss a relationship between representation theory of graded self-injective algebras and that of algebras of finite global dimension. For a positively graded self-injective algebra A   such that A0A0 has finite global dimension, we construct two types of triangle-equivalences. First we show that there exists a triangle-equivalence between the stable category of ZZ-graded A-modules and the derived category of a certain algebra Γ of finite global dimension. Secondly we show that if A has Gorenstein parameter ℓ  , then there exists a triangle-equivalence between the stable category of Z/ℓZZ/ℓZ-graded A-modules and a derived-orbit category of Γ, which is a triangulated hull of the orbit category of the derived category.