Generalized Ihara's lemma for unitary similitude groups

Let $F=F^+E$ be a CM field with $E/{\mathbb Q}$ quadratic imaginary, and let $\overline G$ be the associated unitary similitude group. Let $S$ be a finite set of places and let $\mathbb T_S$ be the unramified Hecke algebra outside $S$. Suppose that $\overline U$ is an open compact subgroup of $\overline G({\mathbb A})$ whose local component outside $S$ is maximal compact, that $w_0\notin S$ is a place decomposed in $E$, and that $\mathfrak m$ is a maximal ideal of $\mathbb T_S$ such that the associated residual representation $\overline\rho_{\mathfrak m}$ is absolutely irreducible. Write $\overline U=\overline U_{w_0}\overline U^{w_0}$. Generalized Ihara's lemma. If $\bar\pi$ is an irreducible subrepresentation of

$$\mathcal C^\oo\left(\overline G({\mathbb Q})\backslash\overline G({\mathbb A})/\overline U^{w_0},\overline{\mathbb F}_l\right)_{\mathfrak m},$$

then its local component $\bar\pi_{w_0}$ at $w_0$ is generic. This is a global form of Ihara's lemma, asserting genericity of the local representation at a split unramified place under an absolute irreducibility hypothesis on the residual Galois representation; the supplied text does not indicate whether the assertion has been proved or remains open.