Geometric Langlands reciprocity conjecture for semisimple groups

Let $G$ be a semisimple group, let $G^\lor$ be its Langlands dual, and let $X$ be the underlying curve. Let $\Lambda$ be the set of isomorphism classes of pairs $(P,\chi)$, where $P$ is a flat $G^\lor$-bundle on $X$ with finite automorphism group $\operatorname{Aut}(P)$, and $\chi$ is an irreducible representation of $\operatorname{Aut}(P)$. Write $\mathcal{N}ilp$ for the global nilpotent cone in $T^*\operatorname{Bun}_G$. For a representation $V$ of $G^\lor$, let $T_{\mathcal{P}(V)}$ denote the Hecke functor and $V_P$ the local system associated with $V$ and $P$. Geometric Langlands reciprocity conjecture. (i) To any $(P,\chi)\in\Lambda$ one can associate a finite set, called an $L$-packet, consisting of $\dim\chi$ perverse sheaves $A$ on $\operatorname{Bun}_G$ whose characteristic variety is contained in $\mathcal{N}ilp$, and such that $T_{\mathcal{P}(V)}(A)=V_P\boxtimes A$. (ii) If the flat bundle $P$ carries a variation of mixed Hodge structure in the sense of Deligne, then the corresponding perverse sheaves on $\operatorname{Bun}_G$ have an additional structure of mixed Hodge modules in the sense of Saito.