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

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Let G be a non-compact semisimple Lie group with finite centre and finitely many 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 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.