Index of nonlocal problems associated with a bundle (Q471416)

In this paper, the authors consider an algebra of operators (already introduced in [the second author and \textit{V. E. Shalatov}, Russ. Acad. Sci., Sb., Math. 81, No. 2, 363--396 (1995); translation from Mat. Sb. 185, No. 3, 117--159 (1994; Zbl 0840.35132)]) associated with a bundle, which contains, in particular, the algebra of pseudo-differential operators on the total space and also the operator of restriction and of integration along the fibers of the bundle. For the elements of this algebra the authors introduce the notion of ellipticity and for the elliptic elements they prove the Fredholm property and derive an index formula.