Segal models for equivariant incomplete infinite loop spaces

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