  The McKay Conjecture (MC) asserts the existence of a bijection between the
(inequivalent) complex irreducible representations of degree coprime to $p$
($p$ a prime) of a finite group $G$ and those of the subgroup $N$, the
normalizer of Sylow $p$-subgroup. In this paper we observe that MC implies the
existence of analogous bijections involving various pairs of algebras,
including certain crossed products, and that MC is \emph{equivalent} to the
analogous statement for (twisted) quantum doubles. Using standard conjectures
in orbifold conformal field theory, MC is \emph{equivalent} to parallel
statements about holomorphic orbifolds $V^G, V^N$. There is a uniform
formulation of MC covering these different situations which involves quantum
dimensions of objects in pairs of ribbon fusion categories.
