The q-Klyachko algebra was introduced lately by Nadeau and Tewari in their study of q-divided symmetrisation. This algebra is equipped with a degree map which computes the q-divided symmetrisation. Inspired by works of Abe--Zeng, Katz--Kutler, and Langer, I will describe two geometric interpretations of the q-Klyachko algebra: a compactified Deligne--Lusztig variety and a toric orbifold. Time permitting, I will also discuss some open problems and directions for further work.