Motivic cohomology of the Nisnevich classifying space of even Clifford groups

Abstract

In this paper, we consider the split even Clifford group ${\Gamma }_n^{+}$ and compute the mod 2 motivic cohomology ring of its Nisnevich classifying space. The description we obtain is quite similar to the one provided for spin groups in [Math. Z. 301 (2022), no. 1, 41–74]. The fundamental difference resides in the behaviour of the second subtle Stiefel–Whitney class that is non-trivial for even Clifford groups, while it vanishes in the spin-case.