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A subset of a discrete group $G$ is called completely Sidon if its span in$C^*(G)$ is completely isomorphic to the operator space version of the space$\ell_1$ (i.e. $\ell_1$ equipped with its maximal operator space structure). Werecently proved a generalization to this context of Drury's classical uniontheorem for Sidon sets: completely Sidon sets are stable under finite unions.We give a different presentation of the proof emphasizing the "interpolationproperty" analogous to the one Drury discovered. In addition we prove theanalogue of the Fatou-Zygmund property: any bounded Hermitian function on asymmetric completely Sidon set $\Lambda\subset G\setminus\{1\}$ extends to apositive definite function on $G$. In the final section, we give a completelyisomorphic characterization of the closed span $C_\Lambda$ of a completelySidon set in $C^*(G)$: the dual (in the operator space sense) of $C_\Lambda$ isexact iff $\Lambda$ is completely Sidon. In particular, $\Lambda$ is completelySidon as soon as $C_\Lambda$ is completely isomorphic (by an arbitraryisomorphism) to $\ell_1(\Lambda)$ equipped with its maximal operator spacestructure.

Interpolation and Fatou-Zygmund property for completely Sidon subsets of discrete groups (New title: Completely Sidon sets in discrete groups)