  A Cayley object for a group G is a structure on which G acts regularly as a
group of automorphisms. The main theorem asserts that a necessary and
sufficient condition for the free abelian group G of rank m to have the generic
n-tuple of linear orders as a Cayley object is that m>n. The background to this
theorem is discussed. The proof uses Kronecker's Theorem on diophantine
approximation.
