In this paper, we study the equivariant homotopy type of a connected sum of linear actions on complex projective planes defined by Hambleton 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 splitting on equivariant homology for general cyclic groups under a divisibility hypothesis, and in all cases for those of prime power order.

The first author would like to thank Surojit Ghosh for some helpful conversations in the proof of Theorem 3.8. The research of the first author was supported by the SERB MATRICS grant 2018/000845. The research of the second author was supported by the NBHM grant no. 16(21)/2020/11. The authors would like to thank the referee for detailed comments about the exposition.