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Let G be an exceptional Lie group with a maximal torus T. Based on commonproperties 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 algebraover the Steenrod algebra A_{p}. The results has been applied in Du2 todetermine the near--Hopf ring structure on the integral cohomology of allexceptional Lie groups.

Schubert calculus and the Hopf algebra structures of exceptional Lie groups