The lattice action conjecture for lattices in special linear groups

Let $\Gamma$ be a lattice in $\mathop{\mathrm{SL}}\nolimits(n,\mathbb{R})$, with $n\geq 3$. Lattice action conjecture. $\Gamma$ has no faithful action on $S^1$. This asks whether Witte's theorem for finite-index subgroups of $\mathop{\mathrm{SL}}\nolimits(n,\mathbb{Z})$ extends to all lattices in $\mathop{\mathrm{SL}}\nolimits(n,\mathbb{R})$; it is open.