  Let $G$ be a linear connected complex reductive Lie group. The purpose of
this paper is to give explicit symplectic isomorphisms from twisted cotangent
bundles of the complex generalized flag varieties, whose transition functions
are given by affine transformations instead of linear transformations, onto the
complex coadjoint semisimple orbits. Moreover, the isomorphisms are shown to be
$G$-equivariant.
