This article deals with the index of Fredholm complexes of -operators of the Hilbert -modulus on C*-algebra. For this class of operators necessary and sufficient conditions in order to be a Fredholm, are obtained. Based on these results, a notion of Fredholm complex and its index is introduced. For this index, a stability theorem related to various perturbations is proved. In the second part of the article, a completation of a semigroup Fredholm complexes is analysed. It is proved that the group K-G (X, Lambda) is the completation of G -Lambda-fibration of the above group on the compact space X.