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Given n, m ∈ ℕ and a simply connected uniform domain U ⊂ ℂ with a sufficiently smooth boundary U , we study the C * -algebra generated by the operators of multiplication by functions in ( ) , by the poly-Bergman projections B U,1 , … , B U,n and by the anti-poly-Bergman projections BU,1 , … , BU,m acting on the Lebesgue space L 2 (U) . The C * -algebra ( ) is generated by the set SO (U) of all bounded continuous functions on U that slowly oscillate at points of U and by the set PC( ) of all piecewise continuous functions on the closure U of U with discontinuities on a finite union of piecewise Dini-smooth curves that have one-sided tangents at every point z ∈ , possess a finite set Y = ∩ U , do not form cusps, and are not tangent to U at the points z ∈ Y . Making use of the Allan-Douglas local principle, the limit operators techniques, quasicontinuous maps, and properties of SO (U) functions, a Fredholm symbol calculus for the C * -algebra U,n,m ( ) is constructed and a Fredholm criterion for its operators is obtained. KeywordsPoly-Bergman and anti-poly-Bergman projections • Piecewise continuous function • Slowly oscillating function • C * -algebra • Fredholm symbol calculus • Fredholmness