Marc Hoyois: Poincaré localizing invariants of schemes

In joint work with Markus Land, we investigate motivic properties of Poincaré localizing invariants of schemes, like Grothendieck-Witt theory, and we establish that they satisfy a projective bundle formula and descent for the Nisnevich topology. This implies that the motivic sphere spectrum over (almost) any local ring R admits a faithful action of the Grothendieck-Witt group of nondegenerate symmetric bilinear forms over R.