The Green–Julg theorem states that 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.
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Walther Paravicini, A generalised Green–Julg theorem for proper groupoids and Banach algebras . J. Noncommut. Geom. 7 (2013), no. 1, pp. 149–190DOI 10.4171/JNCG/112