  We introduce the theory of unipotent morphisms of algebraic stacks. We give
two applications: (1) a unipotent analogue of Gabber's Theorem for torsion
$\mathbf{G}_m$-gerbes and (2) smooth Deligne-Mumford stacks with
quasi-projective coarse spaces satisfy the resolution property in positive
characteristic. Our main tool is a descent result for flags, which we prove
using results of Sch\"appi.
