Multifunctorial Equivariant Algebraic K-Theory

Abstract

A central question in equivariant algebraic K-theory asks whether there exists an equivariant K-theory machine from genuine symmetric monoidal G-categories to orthogonal G-spectra that preserves equivariant algebraic structures. We answer this question positively by constructing an enriched multifunctor K from the G-categorically enriched multicategory of O-pseudoalgebras to the symmetric monoidal category of orthogonal G-spectra, for a compact Lie group G and a 1-connected pseudo-commutative G-categorical operad O. As the main application of its enriched multifunctoriality, K preserves all equivariant algebraic structures parametrized by multicategories enriched in either G-spaces or G-categories. For example, for a finite group G and the G-Barratt-Eccles operad, K transports equivariant E-infinity algebras, in the sense of Guillou-May or Blumberg-Hill, of genuine symmetric monoidal G-categories to equivariant E-infinity algebras of orthogonal G-spectra.