Zhou's connected-components conjecture for Hodge–Newton irreducible affine Deligne–Lusztig varieties

Let $G$ be an adjoint simple group, let $(\lambda,b)$ be a pair consisting of a cocharacter and an element defining an affine Deligne–Lusztig variety $X(\lambda,b)_K$, and let $\eta_G$ be the natural map to $\pi_1(G)_{\Gamma_0}$. Write $\pi_1(G)_{\Gamma_0}^\sigma$ for the set of $\sigma$-fixed points of $\pi_1(G)_{\Gamma_0}$.

Zhou's conjecture. If $(\lambda,b)$ is Hodge–Newton irreducible, then $\eta_G$ induces a bijection

$$\pi_0(X(\lambda,b)_K) \cong \pi_1(G)_{\Gamma_0}^\sigma.$$

This predicts that, in the Hodge–Newton irreducible case, the connected components are completely detected by the fundamental-group obstruction. The supplied text gives no resolution, so the conjecture is left open.