In this talk, we will show that the quotient of a Banach algebra that acts on an L^p space cannot in general be represented on an L^p space whenever p is not equal to 2. This answers a 20 year old question of Le Merdy, and should be contrasted with Junge's partial (affirmative) result for subspaces of L^p spaces. The construction of the (counter)example is not hard, but the proof that it is indeed a counterexample relies on our earlier study of Banach algebras generated by invertible isometries of L^p spaces. This is joint work with Hannes Thiel from the University of Muenster, and a preprint containing the result can be found at: http://arxiv.org/abs/1412.3985