An equivariant Lefschetz fixed-point formula for correspondences

Abstract

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. textitWe dedicate this article to Tamaz Kandelaki, who was a coauthor in an earlier version of this article, and passed away in 2012. We will remember him for his warm character and his perseverance in doing mathematics in difficult circumstances.