  It is a well-known result of Eymard that the Fourier-Stieltjes algebra of a
locally compact group $G$ can be identified with the dual of the group $\cs$
$C^{*}(G)$. A corresponding result for a locally compact groupoid $G$ has been
investigated by Renault, Ramsay and Walter. We show that the Fourier-Stieltjes
algebra $B_{\mu}(G)$ of $G$ (with respect to a quasi-invariant measure $\mu$ on
the unit space $X$ of $G$) can be characterized in operator space terms as the
dual of the Haagerup tensor product
$\ov{L^{2}(X,\mu)}^{r}\otimes_{hA}C^{*}(G,\mu)\otimes_{h A}L^2(X,\mu)^c$ and as
the space of completely bounded bimodule maps
$CB_{A}(C^{*}(G,\mu),B(L^2(X,\mu)))$, where $A=C_{0}(X)$ and $C^{*}(G,\mu)$ is
the groupoid $\cs$ obtained from those $G$-representations associated with
$\mu$. A similar but different result has been given by Renault, but our proof
is along different lines, and full details are given. Examples illustrating the
result are discussed.
