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We show that Chen-Ruan cohomology is a homotopy invariant in certain cases.We introduce the notion of a T-representation homotopy, which is a stringentform of homotopy under which Chen-Ruan cohomology is invariant. We show thatwhile hyperkahler quotients of the cotangent bundle to a complex vector spaceby a circle S^1 (here termed weighted hyperprojective spaces) are homotopyequivalent to weighted projective spaces, they are not S^1-representationhomotopic. Indeed, we show that their Chen-Ruan cohomology rings (over therationals) are distinct.

Weighted hyperprojective spaces and homotopy invariance in orbifold cohomology