# A generalised Green–Julg theorem for proper groupoids and Banach algebras

### Walther Paravicini

University of Münster, Germany

## Abstract

The Green–Julg theorem states that $\mathrm{K}_0^G (B) \cong \mathrm{K}_0(\mathrm{L}^1(G,B))$ for every compact group G and every G-C*-algebra B. We formulate a generalisation of this result to proper groupoids and Banach algebras. This is a key result in the proof that the Bost assembly map is surjective for proper Banach algebra coefficients.

## Cite this article

Walther Paravicini, A generalised Green–Julg theorem for proper groupoids and Banach algebras . J. Noncommut. Geom. 7 (2013), no. 1, pp. 149–190

DOI 10.4171/JNCG/112