Abstract. Let R be an E 2 ring spectrum with zero odd dimensional homotopy groups. Every map of ring spectra M U → R is represented by a map of E 2 ring spectra. If 2 is invertible in π 0 R, then every map of ring spectra M SO → R is represented by a map of E 2 ring spectra.

Abstract. In this paper we give a model for equivariant (∞, 1)-categories. We modify an approach of Shimakawa for equivariant Γ-spaces to the setting of simplicial spaces. We then adapt Rezk's Segal and completeness conditions to fit with this setting.

No abstract