Hochschild cohomology for self-injective algebras of tree class $D_n$. VI

For $R$-bimodule $M$ with $k$-algebra structure and a compatible action of a finite group $G\le\mathrm{Aut}R$ we define algebra $\mathrm{HH}^*(R,M)^{G\uparrow}$. We construct an isomorphism between the algebras $\mathrm{HH^*(R)}$ and $\mathrm{HH}^*(\widetilde R,\widetilde R\#kG)^{G\uparrow}$ in the terms of bar-resolutions, where $\widetilde R=R\#kG^*$. Using these results, we calculate the Hochschild cohomology algebra for a family of self-injective algebras of tree class $D_n$.