Motivic cohomology of the Nisnevich classifying space of even Clifford groups (Q6200599)

Summary: 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 [\textit{F. Tanania}, Math. Z. 301, No. 1, 41--74 (2022; Zbl 1493.14035)]. 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.