TITLE: K-theory for a (geometric) stack
QUESTION [5 upvotes]: There is a notion of $K$-theory for a manifold $M$. 

Is there a notion of $K$-theory for a stack $\mathcal{D}\rightarrow \text{Man}$ that is representable by a Lie groupoid $\mathcal{G}$; that is $B\mathcal{G}\cong \mathcal{D}$?

One reference I could find for $K$-theory for Algebraic stacks is 
Bertrand Toen‘s thesis. Unfortunately, only title and abstract are in English and everything else is in French.
So, are there any references in English that introduce and discuss $K$-theory for stacks. What prerequisites would be needed to understand such theory for stacks?

REPLY [2 votes]: This is written nicely here. The the paper is called Loop Groups and Twisted $K$-theory I, by Freed, Hopkins and Teleman. Have a look at Section 3 and the Appendix.