  Given an $m$-periodic link $L\subset S^3$, we show that the Khovanov spectrum
$\mathcal{X}_L$ constructed by Lipshitz and Sarkar admits a homology group
action. We relate the Borel cohomology of $\mathcal{X}_L$ to the equivariant
Khovanov homology of $L$ constructed by the second author. The action of
Steenrod algebra on the cohomology of $\mathcal{X}_L$ gives an extra structure
of the periodic link. Another consequence of our construction is an alternative
proof of the localization formula for Khovanov homology, obtained first by
Stoffregen and Zhang. By applying Dwyer-Wilkerson theorem we express Khovanov
homology of the quotient link in terms of equivariant Khovanov homology of the
original link.
