  Let E/F be a quadratic number (resp. p-adic) field extension, and F' an odd
degree cyclic field extension of F. We establish a base-change functorial
lifting of automorphic (resp. admissible) representations from the unitary
group U(3,E/F) associated with E/F to the unitary group U(3,F'E/F'). As a
consequence, we classify the invariant packets of U(3,F'E/F'), namely those
which contain (irreducible) automorphic (resp. admissible) representations
which are invariant under the action of the Galois group Gal(F'E/E). To do this
we use the trace formula technique, and well-known results on the base-change
lifting from U(3,E/F) to GL(3,E) and on the base-change lifting for the general
linear groups. We also determine the invariance of individual representations,
using Howe correspondence. This work is the first study of base change into an
algebraic group whose packets are not all singletons, and which does not
satisfy the "strong multiplicity one theorem." Novel phenomena are encountered:
e.g. there are invariant packets where not every irreducible automorphic (resp.
admissible) member is Galois-invariant. We also obtain local twisted character
identities with respect to this base-change lifting.
