Let $G$ be a compact Lie group and $a\in\mathfrak{g}^*$ (dual of Lie algebra of Lie group $G$). Then let $O_a$ be a coadjoint orbit. Then every co-adjoint orbit is Kähler manifolds and also projective variety. How can we compute the Kodaira dimension of co-adjoint orbit as projective variety? Is it $0$