Tits groups of affine Weyl groups

Let G be a connected, reductive group over a non-archimedean local field F. Let F be the completion of the maximal unramified extension of F contained in a separable closure Fₛ. In this article, we construct a Tits group of the affine Weyl group of $G(F)$ when the derived subgroup of GF does not contain a simple factor of unitary type. If G is a quasi-split ramified odd unitary group, we show that there always exist representatives in $G(F)$ of affine simple reflections that satisfy Coxeter relations (which is weaker than asking for the existence of a Tits group). If G = U₂ᵣ, r ≥ 3, is a quasi-split ramified even unitary group, we show that there don't even exist representatives in $G(F)$ of the affine simple reflections that satisfy Coxeter relations.