Dévissage Hermitian Theory

We prove Dévissage theorems for Hermitian $K$ Theory (or $GW$ theory), analogous to Quillen’s Dévissage theorem for $K$-theory. For abelian categories $\mathcal{A}:=(\mathcal{A}{,}^{\vee },\varpi )$ with duality, and appropriate abelian subcategories $\mathcal{B}\subseteq \mathcal{A}$, we prove Dévissage theorems for $\mathbf{G}\mathbf{W}$ spaces, $G\mathcal{W}$-spectra and $\mathbb{G}W$ bispectra. As a consequence, for regular local rings $R$ with $1\mathrm{/}2\in R$, we compute the $\mathbb{G}W$ groups $\mathbb{G}{W}_k^{[n]}(SpecR)$ forall $k,n\in \mathbb{Z}$, where $n$ represent the translation.