A functorial equivariant K-theory spectrum and an equivariant Lefschetz formula

Details A functorial equivariant K-theory spectrum and an equivariant Lefschetz formula A functorial equivariant K-theory spectrum and an equivariant Lefschetz formula

2011-04-18

arxiv.org/abs/1104.3441v1

Mathematics

K-Theory and Homology

20 pages

Scientific paper

We construct a symmetric spectrum representing the G-equivariant K-theory of C*-algebras for a compact group or a proper groupoid G. Our spectrum is functorial for equivariant *-homomorphisms. We use this to establish the additivity of the canonical traces for endomorphisms of strongly dualisable objects in the bootstrap class in equivariant KK, in analogy to previous results for traces in stable homotopy theory. As an application, we prove an equivariant analogue of the Lefschetz trace formula for Hodgkin Lie groups.

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