Equivariant K-theory

Summary

Equivariant K-theory is the version of complex K-theory for spaces with an action of a compact Lie group $G$. It is built from vector bundles on which $G$ acts compatibly with its action on the base. For a point it gives the representation ring of $G$, and for a free action it gives the K-theory of the orbit space. It is the setting of the equivariant index theorem and of the Atiyah–Segal completion theorem.