  We compute the trace of an endomorphism in equivariant bivariant K-theory for
a compact group G in several ways: geometrically using geometric
correspondences, algebraically using localisation, and as a Hattori-Stallings
trace. This results in an equivariant version of the classical Lefschetz
fixed-point theorem, which applies to arbitrary equivariant correspondences,
not just maps.
