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Suppose someone knows well the theory of connected reductive groups, over an algebraically closed field or more generally over any field, say for instance most of the content of Borel-Tits.

Is there a reference on reductive groups with an emphasis on the issues that arise when working with non necessarily connected reductive group ?

I am thinking of something that would give an overview of what part of the theory for connected reductive group extends with little adaptation to the general case, and what part becomes hopelessly wrong in the general case. Also, your own insights on the subject will be welcome as answers.

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Mostow's Annals paper "Selfadjoint groups" considers the problem of which facts (whose proofs are originally exclusive to connected groups) actually extend to possibly disconnected groups, and Platonov/Rapinchuk's book "Number theory and Algebraic groups" also includes several of Mostow's results in this direction. – J. Martel Jun 26 '13 at 17:51
@Joel: Getting an overview from a single source is probably difficult, but for instance there has been a lot of technical literature on how the Deligne-Lusztig representation theory of reductive groups over finite fields adapts to non-connected algebraic groups in that situation. Similarly, the study of conjugacy classes over various fields involves a lot of subtle questions in the non-connected case. This goes back at least to the 1982 Springer Lecture Notes No. 946 by Lusztig's student Spaltenstein. – Jim Humphreys Jun 27 '13 at 0:42

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