TITLE: KK-theoretical proof of Atiyah-Singer index theorem
QUESTION [8 upvotes]: 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!

REPLY [3 votes]: I find the proof in the recent paper of Kasparov 

G. Kasparov. Elliptic and transversally elliptic index theory from the
  viewpoint of KK-theory. J. Noncommut. Geom., 10(4):1303–1378, 2016

difficult but understandable. There are certainly more details than in Kasparov's Inventiones paper.