We study the nonnegative part B_{ \ge 0} of the flag variety of a reductive algebraic group G, as defined by Lusztig. Using positivity properties of the canonical basis it is shown that B_{ \ge 0} has an algebraic cell decomposition indexed by pairs w\le w' of the Weyl group. This result was conjectired by Lusztig in [Lu; Progress in Math 123].
Categories: alg-geom math.AG