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For periodic links, we show that the Khovanov space of Lipshitz-Sarkar admits a natural cyclic group action, and identify its fixed point set. As an application, we prove that the Khovanov homology (with coefficients in the field of p elements) of a p-periodic link has rank greater than or equal to that of the annular Khovanov homology of the quotient link. This is joint work with Melissa Zhang.