Existence and uniqueness of E-infinity structures on motivic K-theory spectra

Abstract

We show that algebraic K-theory KGL, the motivic Adams summand ML and their connective covers acquire unique E-infinity structures refining naive multiplicative structures in the motivic stable homotopy category. The proofs combine Gamma-homology computations and work due to Robinson giving rise to motivic obstruction theory. As an application we employ a motivic to simplicial delooping argument to show a uniqueness result for E-infinity structures on the K-theory Nisnevich presheaf of spectra.