Equivariant homology decompositions for cyclic group actions on definite 4-manifolds

In this paper, we study the equivariant homotopy type of a con-nected sum of linear actions on complex projective planes defined by Ham-bleton and Tanase. These actions are constructed for cyclic groups of odd order. We construct cellular filtrations on the connected sum using spheres inside unitary representations. A judicious choice of filtration implies a split-ting on equivariant homology for general cyclic groups under a divisibility hypothesis, and in all cases for those of prime power order.