  Suppose $F\colon \mathcal{D}(X)\to \mathcal{T}$ is an exact functor from the
bounded derived category of coherent sheaves on a smooth projective variety $X$
to a triangulated category $\mathcal{T}$. If $F$ possesses left and right
adjoints, then the Bondal-Orlov criterion gives a simple way of determining if
$F$ is fully faithful. We prove a natural extension to the case when $X$ is a
smooth and proper DM stack with projective coarse moduli space.
