Stable rank one in nonnuclear crossed products

Abstract

We initiate an investigation into the local structure of simple nonnuclear C$^*$-crossed products by showing that stable rank one is generic within two natural classes of minimal actions of free groups on the Cantor set. The arguments also apply to some other free product groups. Our approach is inspired by Li and Niu's stable rank one theorem in the amenable setting and also yields a streamlined argument in that case, along with a generalization to product actions.