Constructs 2-vector bundles and 2K-theory for Lie groupoids and 2-equivariant settings.
problem Developing a theory of 2-vector bundles and 2K-theory for Lie groupoids and their equivariant versions.
method Defines 2-vector bundles over Lie groupoids, constructs 2K-theory as Grothendieck completion, and proves classification theorems.
result Establishes an equivalence between homotopy categories of 2-vector bundles and simplicial maps, and computes 2-equivariant 2K-theories for specific Lie groups.