Segal models for equivariant incomplete infinite loop spaces

Abstract

We model equivariant infinite loop spaces indexed on incomplete universes via suitable equivariant analogs of $\Gamma$-spaces. The choice of universe dictates a transfer system which in turn dictates the Segal condition on equivariant $\Gamma$-spaces. Equivariant $\Gamma$-spaces themselves come in different but equivalent guises interpolating between categories $\Gamma$ as defined by Segal and $\Gamma_G$ as defined by Shimakawa. The main application is the construction of Segal $K$-theory of normed permutative categories.