  Let $G$ be a locally compact, $\sigma$-compact, Hausdorff groupoid and $A$ be
a separable, $C_0(G^{(0)})$-nuclear, $G$-$C^*$-algebra. We prove the existence
of quasi-invariant, completely positive and contractive lifts for equivariant,
completely positive and contractive maps from $A$ into a separable, quotient
$C^*$-algebra. Along the way, we construct the Busby invariant for $G$-actions.
