  We define and study twisted support varieties for modules over an Artin
algebra, where the twist is induced by an automorphism of the algebra. Under a
certain finite generation hypothesis, we show that the twisted variety of a
module satisfies Dade's Lemma and is one dimensional precisely when the module
is periodic with respect to the twisting automorphism. As a special case we
obtain results on DTr-periodic modules over Frobenius algebras.
