  Let G be a complex connected reductive group. The representation ring R(G)
admits a canonical filtration defined in terms of the lambda-structure. We
compute the associated graded ring gr R(G) (over Q) and the Chern classes of a
representation -- an easy exercise which we have been unable to find in the
literature. As an application we give a simple definition of the characteristic
classes of a principal bundle P --> B in gr K(B), and a simple way of computing
the Chern classes of the associated vector bundles.
