Fixed-point-free involutions on the boundaries of Right-angled Coxeter Groups

About 20 years ago, Bogdan Nica conjectured that the boundary of any word-hyperbolic group admits admits a fixed-point-free involution. In this very short article, we prove a variation of the conjecture, replacing word-hyperbolic groups with Right-angled coxeter groups. This is not a solution to Nica’s conjecture, but hopefully the techniques will shed some light regarding possible approaches to the problem.