I think I got the answer now. The main idea is this: When we gauge continuous symmetries we identify all the states Aμ=Aμ+∂μχ
(which are continuously many) as a unique physical state.
When we gauge a discrete symmetry (let's assume it's generated by θ) we identify all the states
|Ψ⟩=θn|Ψ⟩
where
n=1,…N−1 and
N is the order of the discrete symmetry group. So we identify a finite number of states as a unique physical state. This is exactly what we do when we are orbifolding.
This post imported from StackExchange Physics at 2014-03-31 16:01 (UCT), posted by SE-user Heterotic