We consider solving a given large-scale strictly convex quadratic program by applying the well-known accelerated gradient-projection method to its dual. While this might seem at first sight to be inadvisable since the dual Hessian is defined in terms of the inverse of the primal one, it turns out that all operations may be performed very efficiently so long as a sparse Cholesky factorization of the primal Hessian may be found. In particular, the gradient-projection part of each iteration requires a sequence of ``Cholesky forward solves" with sparse right-hand sides, while the acceleration part may be achieved using, for example, a suitably preconditioned conjugate gradient method. Much use is made of the Fredholm alternative. We illustrate performance of this approach on standard large-scale QP examples, and highlight the methods' use for warm-starting. A new package DQP will shortly be available as part of GALAHAD.