Induction theorems for equivariant K-theory and J-theory
Suppose \(G\) is a group and \(\Lambda\) is a \(G\)-ring, i.e., a ring \(\Lambda\) together with a \(G\)-action on \(\Lambda\) preserving the ring structure. The author introduces notions of a family \(F\) of \(\Lambda\) \(G\)-modules and of \(F\)- projective modules. For each family F, he defines two kinds of equivariant algebraic K-theories \(K^ G(\Lambda,F)_ d\) and \(K^ G(\Lambda,F)_ e\). The approach of this paper is along the line of the classical algebraic K-theory for the purpose of geometric applications. The aim of this paper is to establish the induction theorem for the equivariant algebraic and topological K-theories of this paper and for equivariant J-theory as promised in the author's other paper [Proc. Japan Acad., Ser. A 60, 66-69 (1984; Zbl 0597.20039)].
scientific article; zbMATH DE number 3959734