  We prove that for a self-injective ribbon Grothendieck-Verdier category
$\mathcal{C}$ in the sense of Boyarchenko-Drinfeld the cyclic action on the
Hochschild complex of $\mathcal{C}$ extends to an action of the diffeomorphism
group of the solid closed torus $\mathbb{S}^1 \times \mathbb{D}^2$.
