Let $A$ be a unital $C^*$-algebra. Its unitary group, $UA$, contains a wealth
of topological information about $A$. However, the homotopy type of $UA$ is out
of reach even for $A = M_2(\CC)$. There are two simplifications which have been
considered. The first, well-traveled road, is to pass to $\pi_*(U(A\otimes \KK
))$ which is isomorphic (with a degree shift) to $K_*(A)$. This approach has
led to spectacular success in many arenas, as is well-known.

Let \zeta be an n-dimensional complex matrix bundle over a compact metric
space X and let A_\zeta denote the C*-algebra of sections of this bundle. We
determine the rational homotopy type as an H-space of UA_\zeta, the group of
unitaries of A_\zeta. The answer turns out to be independent of the bundle
\zeta and depends only upon n and the rational cohomology of X. We prove
analogous results for the gauge group and the projective gauge group of a
principal bundle over a compact metric space X.