Twisted \(K\)-theory for actions of Lie groupoids and its completion theorem (Q543338)

The three main contributions of this article are: (1) a definition of twisted equivariant K-theory for actions of groupoids (building on previous work by the author on equivariant K-theory for groupoid actions, and a proof of representability of this theory); (2) a completion theorem for twisted equivariant K-theory; (3) applications to proper actions of Lie groups (context in which twisted equivariant K-theory existed but no completion theorem was known). The paper is very well-written, the exposition clear, succinct and mostly self-contained.