Deligne-Lusztig character theory for general linear groups of rank 2

In this thesis after providing the necessary background in algebraic geometry and algebraic groups we expose the character theory of Deligne and Lusztig for finite groups of Lie type. Then we work out the theory in the case of $GL(2, \ff_{q})$, where $q$ is an odd prime power, and compare the results with the known character tables.