The paper contains comments on the parabolic character sheaves associated to a connected reductive group G, introduced by Lusztig in [L2]. A correspondence is established between parabolic character sheaves and certain perverse sheaves on G, equivariant under a subgroup ¢ of G £ G, acting on G in the usual way (see Th. 3.8). Section 6 is about comments on results of He in [H3
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