Abstract: Let G be a connected complex semi-simple Lie group, and equip it with its standard multiplicative Poisson structure \pi. It is well known that the torus orbits of symplectic leaves of G are the so-called double Bruhat cells G^{u,v}, where u,v are elements of the Weyl group of G. The Poisson structure \pi descends to a Poisson structure on the flag variety G/B, where B is a Borel subgroup of G, and it is also well known that the Bruhat cells BuB/B are Poisson submanifolds of G/B. In this talk, we show that each double Bruhat cell G^{u,u} is a Poisson groupoid over BuB/B, and that each symplectic leaf in G^{u,u} is a symplectic groupoid over BuB/B.  In fact, one can "glue" all the double Bruhat cells in G to obtain a transformation Poisson groupoid over the whole flag variety. This is a joint work with J.-H. Lu.