### A^1-representability of hermitian K-theory and Witt groups, by Jens Hornbostel

We show that hermitian K-theory and Witt groups are representable
both in the unstable and in the stable A^1-homotopy category
of Morel and Voevodsky. In particular, Balmer Witt groups can be nicely
expressed as homotopy groups of a topological space.
The consequences include new results related to
the projective line, blow ups and homotopy purity.
Moreover, this will hopefully become part of a proof of Morel's conjecture
on certain A^1-homotopy groups of spheres, saying in particular
that the endomorphism ring of the motivic sphere spectrum in the stable
A^1-homotopy category should be isomorphic to the Grothendieck-Witt
ring of the base field.

Jens Hornbostel <jens.hornbostel@mathematik.uni-regensburg.de>