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Algebraic and topological K-theory, relations with topology, commutative algebra, and operator algebras
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Relation of $KR(X)$ and $K(Y)$ for $X\to Y$ a $C_2$ principal bundle
It is an important property of usual equivariant $K$-theory that $K_G(X)\cong K(X/G)$ whenever $G$ acts freely on $X$.
What can be said about $KR(X)$ when the action of $C_2$ on $X$ is free? In the co …