[For part I cf. J. Group Theory 6, No. 2, 175-193 (2003; Zbl 1037.20001).]
The paper under review is concerned with equivalences between symmetric algebras (over an algebraically closed field \(k\)) graded by a finite group \(G\). The equivalences are between stable, homotopy and derived module categories. Several results are extended from the ungraded to the graded setting. We mention one of these: Let \(R=\bigoplus_{g\in G}R_g\) be a symmetric crossed product, let \(I\) be a finite \(G\)-set, and let \(X_i \in{\mathcal D}^b (R_1\text{-mod})\), \(i\in I\), be objects satisfying (a) \(\operatorname{Hom}(X_i,X_i[m])=0\) for \(m<0\), (b) \(\operatorname{Hom}(X_i,X_i)=k\) and \(\operatorname{Hom}(X_i,X_j)=0\) for \(i\neq j\), (c) \(X_i\), \(i\in I\), generate \({\mathcal D}^b(R_1\text{-mod})\) as a triangulated category, (d) \(R_g\otimes_{R_1}X_i \cong X_{gi}\) in \({\mathcal D}^b(R_1\text{-mod})\) for \(g\in G\). Then there are a symmetric crossed product \(R'=\bigoplus_{g\in G}R_g'\) and a \(G\)-graded derived equivalence between \(R\) and \(R'\) whose restriction to \(R_1\) sends \(X_i\), \(i\in I\), to the simple \(R_1'\)-modules.