  Let X be a smooth or proper variety defined over a finite field. The
geometric etale fundamental group of X is a normal subgroup of the Weil group,
so conjugation gives it a Weil action. We consider the pro-Q_l-algebraic
completion of the fundamental group as a non-abelian Weil representation.
Lafforgue's Theorem and Deligne's Weil II theorems imply that this affine group
scheme is mixed, in the sense that its structure sheaf is a mixed Weil
representation. When X is smooth, weight restrictions apply, affecting the
possibilities for the structure of this group. This gives new examples of
groups which cannot arise as etale fundamental groups of smooth varieties.
