  We show that a Poisson Lie group $(G,\pi)$ is coboundary if and only if the
natural action of $G\times G$ on $M=G$ is a Poisson action for an appropriate
Poisson structure on $M$ (the structure turns out to be the well known $\pi
_+$). We analyze the same condition in the context of Hopf algebras. Quantum
analogue of the $\pi_+$ structure on SU(N) is described in terms of generators
and relations as an example.
