The Mitchell-Richter filtration of loops on Stiefel manifolds stably splits

We prove that the Mitchell-Richter filtration of the space of loops on complex Stiefel manifolds stably splits. The result is obtained as a special case of a more general splitting theorem. Another special case is H. Miller's splitting of Stiefel manifolds. The proof uses the theory of orthogonal calculus developed by M. Weiss. The argument is inspired by an old argument of Goodwillie for a different, but closely related, general splitting result.