# The Higson-Roe sequence for \'etale groupoids II. The universal sequence for equivariant families

## TL;DR

This paper extends the Higson-Roe sequence to étale groupoids, establishing a universal K-theory surgery exact sequence for transformation groupoids and proving key functoriality and duality properties.

## Contribution

It introduces a universal K-theory surgery exact sequence for étale groupoids, generalizing Higson and Roe's results to transformation groupoids.

## Key findings

- Proved the universal K-theory surgery exact sequence for étale groupoids.
- Established functoriality properties of the sequence.
- Proved the Paschke-Higson duality theorem in this context.

## Abstract

This is the second part of our series about the Higson-Roe sequence for \'etale groupoids. We devote this part to the proof of the universal $K$-theory surgery exact sequence which extends the seminal results of N. Higson and J. Roe to the case of transformation groupoids. In the process, we prove the expected functoriality properties as well as the Paschke-Higson duality theorem.