Quotient triangulated categories

For a self-orthogonal module T, the relation between the quotient triangulated category D-b(A)/K-b(addT) and the stable category of the Frobenius category of T-Cohen-Macaulay modules is investigated. In particular, for a Gorenstein algebra, we get a relative version of the description of the singularity category due to Happel. Also, the derived category of a Gorenstein algebra is explicitly given, inside the stable category of the graded module category of the corresponding trivial extension algebra, via Happel's functor F : D-b (A) -> T (A)(Z)-mod.