I will present an outline of the Carey-Phillips-Rennie-Sukochev approach to the (Odd) Local Index Theorem. Some recent simplifications will be mentioned; as well as numerous amusing stories about Alan Carey.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/111