All algebraic spaces are assumed of finite type over a locally Noetherian base.
Suppose that j:R→X×X is a flat groupoid whose stabilizer j−1Δ is finite over X (where Δ is the diagonal of X×X).
The Keel–Mori theorem states that there is an algebraic space that is a geometric and uniform categorical quotient of X by j, which is separated if j is finite.
A corollary is that for any flat group scheme G acting properly on an algebraic space X with finite stabilizers there is a uniform geometric and uniform categorical quotient X/G which is a separated algebraic space.
János Kollár (1997) proved a slightly weaker version of this and described several applications.