  Consider a Kleinian singularity $ \mathbb{C}^2/\Gamma $, where $ \Gamma $ is
a finite subgroup of $ SL_2(\mathbb{C}) $. In this paper, we construct moduli
spaces of framed sheaves on a projective Deligne-Mumford stack compactifying
the singularity, and we show that these moduli spaces are quasiprojective
schemes.
