  Classically, the exponent of a group is the least common multiple of the
orders of its elements. This notion was generalized by Etingof and Gelaki to
the context of Hopf algebras. Kashina, Sommerhauser and Zhu later observed that
there is a strong connection between exponents and Frobenius-Schur indicators.
In this paper, we introduce the notion of twisted exponents and show that there
is a similar relationship between the twisted exponent and the twisted
Frobenius-Schur indicators defined in previous work of the authors. In
particular, we exhibit a new formula for the twisted Frobenius-Schur indicators
and use it to prove periodicity and rationality statements for the twisted
indicators.

Quantum Algebra;Representation Theory