This paper, coauthored by Martin Bendersky, was accepted to appear in Boletin Sociedad Matematicas Mexicana on Sept 23, 2005. Here it is in pdf format.
Abstract: In a recent paper, 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. 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 v1-map when n is odd. There are a few extreme cases which we are unable to determine precisely.