I am reading [Differentiable Stacks, Gerbes, and Twisted K-Theory][1] by Ping Xu.

To talk about (twisted) K-theory of Differentiable stacks, author introduced (page $41$) the set up of $C^*$-algebras. All I know about $C^*$-algebras is their definition and one or two results. 

Can some one suggest me some other reference where there is some (partially) detailed explanation of appearance (and necessity) of $C^*$-algebras in the study of Lie groupoids/Differentiable Stacks?

Is there any  set up of special case of Lie groupoids, say manifolds, where the appearance of $C^*$-algebras is already a standard notion? Any references for this would also be very useful.


 

  [1]: http://www.personal.psu.edu/pxx2/book.pdf