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Let $G=K\ltimes A$ be the semi-direct product group of a compact group $K$acting on an abelian locally compact group $A$. We describe the $C^*$-algebra$C^*(G)$ of $G$ in terms of an algebra of operator fields defined over thespectrum of $G $, generalizing previous results obtained for some specialclasses of such groups.

The C*-algebra of the semi-direct product K and A