Existence and uniqueness of E_{ } E ∞ structures on motivic K K -theory spectra

Abstract

We show that algebraic K-theory KGL , the motivic Adams summand and their connective covers acquire unique 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.