(untitled) (Annual of Sofia University St. Kliment Ohridski. Faculty of Mathematics and Informatics, 2021)
We consider the groupoid C^*-algebra T = C^*(G), where the groupoid G is a reduction of a transformation group G = (Y × G)|X, and Y and X are suitable topological spaces. We impose additional constraints on a cross-section ψ, which gives opportunity to define cyclic 1-cocycle and to obtain a formula that calculates the index of the Fredholm operators.