Author 1: A. Broer email: broera@DMS.UMontreal.CA Address: D\'epartement de math\'emathiques et de statistique Universit\'e de Montr\'eal C.P. 6128, succursale Centre-ville Montr\'eal (Qu\'ebec), Canada H3C 3J7 Author 2: V. Reiner email: reiner@math.umn.edu Address: School of Mathematics, University of Minnesota, Minneapolis MN 55455 Author 3: Larry Smith email: larry@uni-math.gwdg.de Address: Mathematisches Institut Bunsenstrasse 3-5 D 37073 Goettingen Federal Republic of Germany Author 4: P. Webb email: webb@math.umn.edu Address: School of Mathematics, University of Minnesota, Minneapolis MN 55455 Title: Extending the coinvariant theorems of Chevalley, Shephard-Todd, Mitchell, and Springer Abstract: We extend in several directions invariant theory results of Chevalley, Shephard and Todd, Mitchell and Springer. Their results compare the group algebra for a finite reflection group with its coinvariant algebra, and compare a group representation with its module of relative coinvariants. Our extensions apply to arbitrary finite groups in any characteristic. Preprint May 2008.