This is the second part of the second volume of the monograph devoted by the authors to non-local problems. For the review of Part 1 see Zbl 0936.35211 above.
From the abstract point of view, operators under consideration are of the form \[ P=\sum p_gU_g \] where \(p_g\) belongs to an algebra \(A\) of operators and \(T_g\), with \(g\in G\), are the shift operators, forming a representation of a group \(G\) and generating a group of automorphisms of \(A\). In the present volume, \(A\) is the algebra of the pseudo-differential operators with piecewise continuous coefficients, or the algebra of the Boutet de Monvel operators, describing general pseudo-differential boundary value problems. Toeplitz operators with piecewise continuous coefficients are also considered. A third volume is announced, concerning functional differential equations and \(C^*\) algebras related to endomorphisms, and operators in \(L^p\) spaces.