Stably Cayley semisimple groups.
A linear algebraic group over a field is called a Cayley group if it admits a Cayley map, i.e., a -equivariant birational isomorphism over between the group variety and its Lie algebra Lie. A prototypical example is the classical "Cayley transform" for the special orthogonal group defined by Arthur Cayley in 1846. A linear algebraic group is called stably Cayley if is Cayley for some split -torus . We classify stably Cayley semisimple groups over an arbitrary field of characteristic 0.