A cellular absolute motivic ring spectrum representing Hermitian K-theory

Abstract: Several candidates for a motivic spectrum representing hermitian K-theory in the Morel-Voevodsky motivic stable homotopy category over schemes in which 2 is not necessarily invertible exist. This note shows that the cellular absolute motivic spectrum constructed in the thesis of the first author via the geometry of orthogonal and hyperbolic Grassmannians over any scheme coincides with the motivic ring spectrum constructed recently by Calm`es, Harpaz, and Nardin.