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