Multiplicative Hitchin Fibrations and the Fundamental Lemma

Let $k$ be a finite field and let $G$ be a reductive group over $k[[\pi ]]$. Suppose $\mathrm{c}\mathrm{h}\mathrm{a}\mathrm{r}(k)$ is larger than twice the Coxeter number of $G$, we prove the standard endoscopic fundamental lemma for the spherical Hecke algebra of $G$ using multiplicative Hitchin fibrations.