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.