  We show that when a torus $T$ acts on a smooth variety $X$, the twisted HKR
isomorphism is equivariant. The main consequence is that the Bezrukavnikov-
Lachowska isomorphism, relating the Hochschild cohomology of the principal
block of the small quantum group to certain sheaf cohomology groups on the
Springer resolution $\widetilde{\mathcal{N}}$ , can be upgraded to a ring
isomorphism by a twist.
