Doctor of Philosophy
We give a definition of a root stack and describe its most basic properties. Then we recall the necessary background (Abhyankar’s lemma, Chevalley-Shephard-Todd theorem, Luna’s etale slice theorem) and prove that under some conditions a quotient stack is a root stack. Then we compute G-theory and K-theory of a root stack. These results are used to formulate the theorem on equivariant algebraic K-theory of schemes.
Kobyzev, Ivan, "K-Theory Of Root Stacks And Its Application To Equivariant K-Theory" (2016). Electronic Thesis and Dissertation Repository. 3923.