Polya Theory for Orbiquotient Sets

Replacing the usual notion of quotient sets by the notion of orbiquotient sets we obtain a generalization of P\'olya theory. The key ingredient of our extended theory is the definition of the orbicycle index polynomial which we compute in several examples. We apply our theory to the study of orbicycles on orbiquotient sets. Keywords: Orbifolds, P\'olya Theory, Partition Lattice.