  Given a two-dimensional conformal field theory with a global symmetry, we
propose a method to implement an orbifold construction by taking orbits of the
modular group. For the case of cyclic symmetries we find that this approach
always seems to be consistent, even in asymmetric orbifold cases where the
usual construction does not yield a modular invariant theory; our approach
keeps modular invariance manifest but may give a result that is equivalent to
the original theory. For the case that the symmetry is a subgroup of a
continuous flavor symmetry, we can give explicit constructions of the spectrum,
with twisted sectors corresponding to a non-standard group projection on an
enlarged twisted sector Hilbert space.
