Oblomkov–Yun quasi-split extension conjecture

Let $\mathbb{G}$ be a quasi-split generic group, and let the local systems, perverse filtrations, rational DAHA actions, and braid-group actions be defined as in the split case. Oblomkov–Yun's quasi-split extension conjecture. The constructions and the invariant-simple-module theorem for split $\mathbb{G}$ should extend to quasi-split $\mathbb{G}$, while retaining the further stated properties of the perverse filtration. This would extend the affine-Springer and rational-DAHA picture beyond split groups; the supplied text gives no resolution status.