The charfiniteness conjecture for higher-rank lattices

Let $\Gamma$ be an irreducible higher-rank lattice. The charfiniteness conjecture. The group $\Gamma$ is charfinite, in the sense of the character-rigidity terminology used in the source. The source states that irreducible higher-rank lattices are charmenable and conjectures charfiniteness; the definition of charfinite is not supplied here.