Equivariant Kasparov theory of finite groups via Mackey functors

Details Equivariant Kasparov theory of finite groups via Mackey functors Equivariant Kasparov theory of finite groups via Mackey functors

2011-05-16

arxiv.org/abs/1105.3028v1

Mathematics

Operator Algebras

28 pages

Scientific paper

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.

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