I am reading Differentiable Stacks, Gerbes, and Twisted K-Theory 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.

I am reading Differentiable stacks, gerbes, and twisted K-Theory 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.