  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 stringent
form of homotopy under which Chen-Ruan cohomology is invariant. We show that
while hyperkahler quotients of the cotangent bundle to a complex vector space
by a circle S^1 (here termed weighted hyperprojective spaces) are homotopy
equivalent to weighted projective spaces, they are not S^1-representation
homotopic. Indeed, we show that their Chen-Ruan cohomology rings (over the
rationals) are distinct.
