Automorphy of $m$-fold tensor products of GL(2)

We prove that for any m > 1 , given any m -tuple of Hecke eigenforms f_i of level 1 whose weights satisfy the usual regularity condition, there is a self-dual cuspidal automorphic form \pi of {\rm GL}_{2^m}(\mathbb{Q}) corresponding to their tensor product, i.e., such that the system of Galois representations attached to \pi agrees with the tensor product of the ones attached to the cuspforms f_i .