  We characterize Riemannian orbifolds with an upper curvature bound in the
Alexandrov sense as reflectofolds, i.e. Riemannian orbifolds all of whose local
groups are generated by reflections, with the same upper bound on the sectional
curvature. Combined with a result by Lytchak--Thorbergsson this implies that a
quotient of a Riemannian manifold by a closed group of isometries has locally
bounded curvature (from above) in the Alexandrov sense if and only if it is a
reflectofold.
