In their book [Cutting and pasting of manifolds; \(SK\)-groups. Math. Lect. Ser. 1 (1973; Zbl 0258.57010)] U. Karras, M. Kreck, W. D. Neumann and E. Ossa introduced the notion of cutting and pasting of manifolds and the \(SK\)-group to investigate \(SK\)-invariants, i.e., invariants under cutting and pasting of manifolds. The author of the paper under review studies the equivariant case with \(G_r\)-actions, where \(G_r\) is the cyclic group of order \(2^r\). He shows that the \(G_r\)-\(SK\)-group is a free \(SK_*\)-module, and obtains the set of generators explicitly. He also discusses \(G_r\)-\(SK\)-invariants and obtains a complete set of such invariants.