  We consider a version of the $AdS_{d+1}/CFT_{d}$ correspondence, in which the
bulk space is taken to be the quotient manifold $AdS_{d+1} /\Gamma$ with a
fairly generic discrete group $\Gamma$ acting isometrically on $AdS_{d+1}$. We
address some geometrical issues concerning the holographic principle and the
UV/IR relations. It is shown that certain singular structures on the quotient
boundary ${\bf S}^{d}/\Gamma$ can affect the underlying physical spectrum. In
particular, the conformal dimension of the most relevant operators in the
boundary CFT can increase as $\Gamma$ becomes ``large''. This phenomenon also
has a natural explanation in terms of the bulk supergravity theory. The scalar
two-point function is computed using this quotient version of the AdS/CFT
correspondence, which agrees with the expected result derived from conformal
invariance of the boundary theory.
