  We report on two classes of autoequivalences of the category of
Yetter-Drinfeld modules over a finite group, or, equivalently the Drinfeld
center of the category of representations of a finite group. Both operations
are related to the $r$-th power operation, with $r$ relatively prime to the
exponent of the group. One is defined more generally for the group-theoretical
fusion category defined by a finite group and an arbitrary subgroup, while the
other seems particular to the case of Yetter-Drinfeld modules. Both
autoequivalences preserve higher Frobenius-Schur indicators up to Galois
conjugation, and they preserve tensor products, although neither of them can in
general be endowed with the structure of a monoidal functor.
