The conjecture on endoscopic equivalence without restrictions on $\ell$

Let $\mathbf{G}$ be the reductive group, let $\mathrm{F}$ be its Frobenius morphism, and let $\ell$ be the coefficient characteristic. Let the endoscopic equivalence refer to the equivalence constructed in Theorem

$$of the source. **Endoscopic equivalence conjecture.** There \exists an endoscopic equivalence as in Theorem$$

without any hypothesis on $\ell$.

The conjecture seeks to remove the restrictions on $\ell$ needed in the construction of the endoscopic equivalence. The source states that the generalization is conjectural and explains that the existing proof uses hypotheses on $\ell$ in two places; it therefore remains open.