Grothendieck-Witt groups of some singular schemes

We establish some structural results for the Witt and Grothendieck-Witt groups of schemes over $\mathbb{Z}[1\mathrm{/}2]$, including homotopy invariance for Witt groups and a formula for the Witt and Grothendieck-Witt groups of punctured affine spaces over a scheme. All these results hold for singular schemes and at the level of spectra.