## Annals of K-Theory

### Algebraic $K$-theory of quotient stacks

#### Abstract

We prove some fundamental results like localization, excision, Nisnevich descent, and the regular blow-up formula for the algebraic $K$-theory of certain stack quotients of schemes with affine group scheme actions. We show that the homotopy $K$-theory of such stacks is homotopy invariant. This implies a similar homotopy invariance property of the algebraic $K$-theory with coefficients.

#### Article information

Source
Ann. K-Theory, Volume 3, Number 2 (2018), 207-233.

Dates
Received: 12 October 2016
Revised: 17 July 2017
Accepted: 1 August 2017
First available in Project Euclid: 4 April 2018

Permanent link to this document
https://projecteuclid.org/euclid.akt/1522807258

Digital Object Identifier
doi:10.2140/akt.2018.3.207

Mathematical Reviews number (MathSciNet)
MR3781427

Zentralblatt MATH identifier
06861673

#### Citation

Krishna, Amalendu; Ravi, Charanya. Algebraic $K$-theory of quotient stacks. Ann. K-Theory 3 (2018), no. 2, 207--233. doi:10.2140/akt.2018.3.207. https://projecteuclid.org/euclid.akt/1522807258

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