$\mathrm{C}^*$-selflessness of vigorous groups

Abstract: We prove that countable groups which admit a faithful piecewise minimal-extremely-proximal action on the Cantor set are $\mathrm{C}<sup>*$-selfless. In particular, topological full groups of second countable, Hausdorff, minimal, purely infinite, topologically principal, ample groupoids with compact unit spaces are $\mathrm{C}<sup>*$-selfless. Examples include the Higman--Thompson groups and the Brin--Thompson groups.