Geodesic
Representations of Banach algebras and formulas of Hirzebruch type
Sbornik. Mathematics, Tome 39 (1981) no. 2, pp. 189-205

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A description of Fredholm representations as a particular case of graded representations is given. For graded representations of Banach algebras Hirzebruch type formulas are deduced by the method of bordism theory and the theory of bundles of algebraic Poincaré complexes. Bibliography: 13 titles. 
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     author = {A. S. Mishchenko and Yu. P. Solov'ev},
     title = {Representations of {Banach} algebras and formulas of {Hirzebruch} type},
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A. S. Mishchenko; Yu. P. Solov'ev. Representations of Banach algebras and formulas of Hirzebruch type. Sbornik. Mathematics, Tome 39 (1981) no. 2, pp. 189-205. http://geodesic.mathdoc.fr/item/SM_1981_39_2_a2/