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

We show that algebraic (Formula presented.) -theory (Formula presented.) , the motivic Adams summand (Formula presented.) and their connective covers acquire unique (Formula presented.) structures refining naive multiplicative structures in the motivic stable homotopy category. The proofs combine (Formula presented.) -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 (Formula presented.) structures on the (Formula presented.) -theory Nisnevich presheaf of spectra.