An algebraic group G is geometrically reductive if for every nonzero G-invariant vector v in a G-representation V, there exists a non-constant homogeneous G-invariant polynomial function on V which does not vanish on v. We will see Haboush's proof that every reductive group is geometrically reductive. The main character of this proof is the Steinberg representation; the bulk of the talk will be about this representation. Speaker(s): Karthik Ganapathy (UM)