  Let G be a finite group. We systematically exploit general homological
methods in order to reduce the computation of G-equivariant KK-theory to
topological equivariant K-theory. The key observation is that the functor
assigning to a separable G-C*-algebra the collection of all its equivariant
K-theory groups lifts naturally to a homological functor taking values in the
abelian tensor category of Mackey modules over the classical representation
Green functor for G. This fact yields a new universal coefficient and a new
Kuenneth spectral sequence for the G-equivariant Kasparov category, whose
convergence behavior is nice for all G-C*-algebras in a certain bootstrap
class.
