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Does anyone know of any detailed proof of the Atiyah-Singer Index Theorem using KK-theory/ Kasparov products? References to any papers and textbooks are greatly appreciated. Thanks!

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    $\begingroup$ A standard reference is A. Connes and G. Skandalis paper alainconnes.org/docs/longitudinal.pdf. The paper does the index theorem for foliations as well but you can only read the first 3 chapters. $\endgroup$ – Omar Jan 16 '18 at 10:31

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