Arthur–Langlands conjecture for semisimple groups

Let $G$ be a semisimple $\mathbb{Q}$-group admitting a reductive $\mathbb{Z}$-model. Let $\pi\in\Pi_{\mathrm{disc}}(G)$ and let $r:\widehat{G}\to\mathrm{SL}_{n,\mathbb{C}}$ be an algebraic representation. Arthur–Langlands conjecture. There exist integers $k\geq1$, $n_i,d_i\geq1$, and cuspidal representations $\pi_i\in\Pi_{\mathrm{cusp}}(\operatorname{PGL}_{n_i})$ such that

$$n=\sum_{i=1}^{k}n_i d_i,$$

and

$$\psi(\pi,r)=\pi_1[d_1]\oplus\cdots\oplus\pi_k[d_k].$$

Here $\psi(\pi,r)$ is the global parameter obtained from $r$ and $\pi$, and $\pi_i[d_i]$ denotes the tensoring of $\pi_i$ with the $(d_i)$-dimensional symmetric-power parameter. The conjecture predicts the stated decomposition for every such $G$, $\pi$, and $r$; no resolution status is specified in the source.