# Each coadjoint orbit of a compact connected Lie group $G$ admits a $G$-invariant generalized complex structure

I am looking for a proof or counterexample for following assertion

Each coadjoint orbit of a compact connected Lie group $G$ admits a $G$-invariant generalized complex structure (In sense of Nigel Hitchin)

In 1950s A. Borel, R. Bott, J. L. Koszul, F. Hirzebruch et al. investigated the coadjoint orbits as complex homogeneous manifolds. It was proven that each coadjoint orbit of a compact connected Lie group $G$ admits a canonical G-invariant complex structure and the only (within homotopies) $G$-invariant Kählerian metrics.