Stable geometric dimension of vector bundles over odd-dimensional real projective spaces

In [6], the geometric dimension of all stable vector bundles over real projective space P-n was determined if n is even and sufficiently large with respect to the order 2(e) of the bundle in (KO) over tilde (P-n). Here we perform a similar determination when n is odd and e > 6. The work is more delicate since P-n does not admit a nu(1)-map when n is odd. There are a few extreme cases which we are unable to settle precisely.