LAUSR

In this paper, we compute the $$RO(C_{pq})$$RO(Cpq)-graded cohomology of $$C_{pq}$$Cpq-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 $$C_p$$Cp. The computations of cohomology of orbits are used to prove a freeness theorem. The analogous result for the group $$C_p$$Cp was proved by Lewis. We demonstrate that certain complex projective spaces and complex Grassmannians satisfy the freeness theorem.