  We develop an Eilenberg-Moore spectral sequence to compute Bredon cohomology
of spaces with an action of a group given as a pullback. Using several other
spectral sequences, and positive results on the Baum-Connes Conjecture, we are
able to compute Equivariant K-theory and K-Homology of the reduced group
C*-algebra of a 6-dimensional crystallographic group $\Gamma$ introduced by
Vafa and Witten. We also use positive results on the Farrell-Jones Conjecture
to give a vanishing result for the negative algebraic K-theory of the integral
group ring of $\Gamma$.
