  We refine the notion of variety over the "field with one element" developed
by C. Soul\'e by introducing a grading in the associated functor to the
category of sets, and show that this notion becomes compatible with the
geometric viewpoint developed by J. Tits. We then solve an open question of C.
Soul\'e by proving, using results of J. Tits and C. Chevalley, that Chevalley
group schemes are examples of varieties over a quadratic extension of the above
"field".
