Twisted conjugacy and quasi-isometric rigidity of irreducible lattices in semisimple lie groups

Let G be a non-compact semisimple Lie group with finite centre and finitely many connected components. We show that any finitely generated group Γ which is quasi-isometric to an irreducible lattice in G has the R ∞ -property, namely, that there are infinitely many ϕ -twisted conjugacy classes for every automorphism ϕ of Γ. Also, we show that any lattice in G has the R ∞ -property, extending our earlier result for irreducible lattices.