| Summary: | The C∗-algebra B of bounded linear operators on the space L2}T, which is generated by all multiplication operators by piecewise quasicontinuous functions, by the Cauchy singular integral operator and by the range of a unitary representation of a group G of orientation-preserving diffeomorphisms of T onto itself that have the same finite set of fixed points for all (Formula presented), is studied. A Fredholm symbol calculus for the C∗-algebra B and a Fredholm criterion for the operators (Formula presented) are established by using spectral measures and the local-trajectory method for studying C∗-algebras associated with C∗-dynamical systems.
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