On the Hermitian K-theory of Grassmannians

We compute the $\mathbb{G}W$-spectrum (Karoubi--Grothendieck--Witt spectrum) of Grassmannians over divisorial schemes defined over fields of characteristic zero, and, as a corollary, determine their stabilized $\mathbb{L}$-theory spectrum. As part of our computation, we establish split fibration sequences in $\mathbb{K}$-theory, $\mathbb{G}W$-theory and $\mathbb{L}$-theory.