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We construct a symmetric spectrum representing the G-equivariant K-theory ofC*-algebras for a compact group or a proper groupoid G. Our spectrum isfunctorial for equivariant *-homomorphisms. We use this to establish theadditivity of the canonical traces for endomorphisms of strongly dualisableobjects in the bootstrap class in equivariant KK, in analogy to previousresults for traces in stable homotopy theory. As an application, we prove anequivariant analogue of the Lefschetz trace formula for Hodgkin Lie groups.

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