  Let G be a finite group. Over any finite G-poset P we may define a
transporter category as the corresponding Grothendieck construction. The
classifying space of the transporter category is the Borel construction on the
G-space BP, while the k-category algebra of the transporter category is the
(Gorenstein) skew group algebra on the G-incidence algebra kP.
  We introduce a support variety theory for the category algebras of
transporter categories. It extends Carlson's support variety theory on group
cohomology rings to equivariant cohomology rings. In the mean time it provides
a class of (usually non selfinjective) algebras to which Snashall-Solberg's
(Hochschild) support variety theory applies. Various properties will be
developed. Particularly we establish a Quillen stratification for modules.
