  We show that Tolman's example (of a six dimensional Hamiltonian $T^2$-space
with isolated fixed points and no compatible K\"{a}hler structure) can be
constructed from the flag variety $U(3)/U(1)^3$ by $U(2)$-equivariant
symplectic surgery. This implies that Tolman's space has a ``transversal
multiplicity-free'' action of $U(2)$ and that Delzant's theorem ``every compact
multiplicity-free torus action is K\"{a}hler'' \cite{D1} does not generalize to
non-abelian actions.
