Transfers on ${\mathbb{A}}^1$-connected components of quasi-split groups and the norm principle

Abstract

We show that the sheaf of ${\mathbb{A}}^1$-connected components of a quasi-split group over a perfect field is a strictly ${\mathbb{A}}^1$-invariant sheaf with (Voevodsky) transfers. As a consequence, we show that the norm principle holds for any quasi-split group over a perfect field.

12 pages, v2: some inaccuracies removed, minor modifications, main results unchanged, comments are welcome