An Equivariant Lefschetz Fixed-Point Formula for Correspondences

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. \textit{We 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.}

2010 Mathematics Subject Classification: 19K99, 19K35, 19D55

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