  In this note we investigate the idea of Michael Atiyah of using, as a
possible approach to the Theorem of Feit-Thompson on the solvability of finite
groups of odd order, the iterations of the transformation which replaces a
representation of a finite group G on a finite dimensional complex vector space
E by the difference between the associated representation of G on the sum of
exterior powers of E and the trivial representation. We show that G has odd
order if and only if the above operation extends to virtual representations and
we then express it in terms of the exponential and the Adams operations in the
complexified representation ring. We show the relevance of the idea in a
concrete example by exhibiting convergence to a non-trivial character.
