Equivariant Khovanov homotopy type

Given a link L in S^3, Lipshitz and Sarkar constructed a suspension spectrum X_L whose stable homotopy type is an invariant of L.
When the link is periodic, i.e. it admits a special type of rotational symmetry, it is natural to ask whether this symmetry descends to X_L.

In may talk I will sketch how to extend the construction of Lipshitz and Sarkar in order to incorporate the group action.
I will also discuss invariance of the resulting equivariant spectrum under equivariant isotopies of links and its relation to equivariant Khovanov homology.