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Replaces Previous version. Includes comments on poincare duality for twistedequivariant in the context of proper and discrete actions and the Baum-ConnesConjecture. We use a spectral sequence proposed by C. Dwyer and previous workby Sanchez-Garcia and Soule to compute Twisted Equivariant K-theory groups ofthe classifying space for proper actions of Sl3(Z). After proving a Universalcoefficient theorem in Bredon Cohomology with specific coefficients, we computethe twisted equivariant K-homology and state a relation to the Baum-ConnesConjecture with coefficients.

Twisted equivariant K- Theory and K-Homology of Sl3(Z)