  Let G be an exceptional Lie group with a maximal torus T. Based on common
properties in the Schubert presentation of the cohomology ring H*(G/T;F_{p})
DZ1, and concrete expressions of generalized Weyl invariants for G over F_{p},
we obtain a unified approach to the structure of H*(G;F_{p}) as a Hopf algebra
over the Steenrod algebra A_{p}. The results has been applied in Du2 to
determine the near--Hopf ring structure on the integral cohomology of all
exceptional Lie groups.
