Infinite loop G-spaces associated to monoidal G-graded categories (Q1123442)

Summary: We construct a functor \(K_ G\) which takes each pair of monoidal G- graded categories \((D,D')\) to an infinite loop G-space \(K_ G(D,D')\). When \(D'=D\), its homotopy groups \(\pi_ n^ GK_ G(D,D)\) coincide with equivariant K-groups \(K_ nRep D\) of D. Applications include the simple construction of equivariant infinite deloopings of the maps \(BO(G)\to BPL(G)\to BTop(G)\) between equivariant classifying spaces.