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Background results;
1. Bruhat decomposition;
2. Reduced subgroups of maximal rank, centralisers and semisimple elements;
3. Rationality, Frobenius maps, Lang's theorem;
4. Generalized induction associated with a bimodule;
5. Mackey's theorem;
6. Harish-Chandra theory; Complements on RGL;
7. Duality of characters;
8. Steinberg characters; l-adic cohomology;
9. Deligne-Lusztig induction;
10. Character formulae and their complements in Deligne-Lusztig induction;
11. Geometric conjugation, Lusztig series.
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