We compare twisted equivariant K-theory of SL 3 Z with untwisted equivariant K-theory of a central extension St 3 Z.We compute all twisted equivariant K-theory groups of SL 3 Z, and compare them with previous work on the equivariant K-theory of BSt 3 Z by Tezuka and Yagita.Using a universal coefficient theorem by the authors, the computations explained here give the domain of Baum-Connes assembly maps landing on the topological K-theory of twisted group C * -algebras related to SL 3 Z, for which a version of KKtheoretic duality studied by Echterhoff, Emerson, and Kim is verified.