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Higher equivariant \(K\)-theory for finite group actions. (English) Zbl 0738.55002

Let \(X\) be a separated, Noetherian, regular scheme over a field, \(K\), of characteristic \(p\). Let \(G\) be a finite group which acts on \(X\) and let \(n=L\subset M\{\hbox{order}(g)\mid g\in G\}\). Suppose that \(K\) contains all \(p\)-primary roots of unity whose order divides \(n\). Set \(\Lambda=\mathbb{Z}[| G|^{-1}]\) and let \(K_ *(X//G)\) denote the equivariant algebraic \(K\)-theory of \(X\). The author obtains a decomposition of \(K_ *(X//G)\otimes\Lambda\) indexed by the conjugacy classes of cyclic subgroups of \(C\). This decomposition is analogous to one obtained for the topological equivariant \(K\)-theory of a \(G\)- manifold.

MSC:

55N15 Topological \(K\)-theory
55N91 Equivariant homology and cohomology in algebraic topology
19L47 Equivariant \(K\)-theory
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