  Let A be a finite-dimensional, self-injective algebra, graded in non-positive
degree. We define A-dgstab, the differential graded stable category of A, to be
the quotient of the bounded derived category of dg-modules by the thick
subcategory of perfect dg-modules. We express A-dgstab as the triangulated hull
of the orbit category A-grstab/$\Omega$(1). This result allows computations in
the dg-stable category to be performed by reducing to the graded stable
category. We provide a sufficient condition for the orbit category to be
equivalent to A-dgstab and show this condition is satisfied by Nakayama
algebras and Brauer tree algebras. We also provide a detailed description of
the dg-stable category of the Brauer tree algebra corresponding to the star
with n edges.
