This is a preliminary report on joint work with Greg Lupton, Chris Phillips and Claude Schochet. The goal is to study the sensitivity of rational homotopy theory as an invariant for C*-algebras. As a test case, we consider the following example: Let p : E \to X be a matrix bundle over a compact space X. Let A be the C*-algebra of sections of the bundle and UA the group of unitaries in A. We determine the Sullivan model of UA for certain formal spaces X and show the model for UA detects the Chern classes of the bundle.