  For a self-orthogonal module $T$, the relation between the quotient
triangulated category $D^b(A)/K^b({\rm add} T)$ 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 $F: D^b(A) \longrightarrow
T(A)^{\mathbb{Z}}{-}\underline{\rm mod}$.
