Computations in Cpq-Bredon cohomology.

In this paper, we compute the R O (C pq) -graded cohomology of C pq -orbits. We deduce that in all the cases the Bredon cohomology groups are a function of the fixed point dimensions of the underlying virtual representations. Further, when thought of as a Mackey functor, the same independence result holds in almost all cases. This generalizes earlier computations of Stong and Lewis for the group C p . The computations of cohomology of orbits are used to prove a freeness theorem. The analogous result for the group C p was proved by Lewis. We demonstrate that certain complex projective spaces and complex Grassmannians satisfy the freeness theorem. [ABSTRACT FROM AUTHOR]