Gross's Euler–Poincaré orbital-integral conjecture

Let $F$ be a non-Archimedean local field, let $G$ be the reductive group under consideration, and let $f^{EP}$ be the Euler–Poincaré function with respect to a Haar measure $dg$ on $G(F)$. For a semisimple element $\gamma$ with centralizer $G_\gamma(F)$, write $O_\gamma(f^{EP},dg/dg_\gamma)$ for its orbital integral, let $dg_\gamma$ be any Haar measure on $G_\gamma(F)$, and let $dg_\gamma^{EP}$ be the Euler–Poincaré measure on $G_\gamma(F)$. Gross's Euler–Poincaré conjecture.

$$O_\gamma(f^{EP},dg/dg_\gamma)dg_\gamma=\begin{cases}dg_\gamma^{EP}&\text{if }\gamma\text{ is elliptic semisimple},\\0&\text{otherwise.}\end{cases}$$

The conjecture identifies the orbital integrals of the Euler–Poincaré function with Euler–Poincaré measures precisely on elliptic semisimple classes. It is attributed here to Gross; the supplied text does not state whether it has been resolved.