  A weakly equivariant Hopf algebra is a Hopf algebra A with an action of a
finite group G up to inner automorphisms. We show that each weakly equivariant
Hopf algebra can be replaced by a Morita equivalent algebra B with a strict
action of G and with a coalgebra structure that leads to a tensor equivalent
representation category. However, the coproduct of this strictification cannot,
in general, be chosen to be unital, so that a strictification of the G-action
can only be found on a weak Hopf algebra B.
