  We show that representations of convolution algebras such as Lustzig's graded
affine Hecke algebra or the quiver Hecke algebra and quiver Schur algebra in
(affine) type A can be realised in terms of certain equivariant motivic sheaves
called Springer motives. To this end, we lay foundations to a motivic Springer
theory and prove formality results using weight structures.
  As byproduct, we express Koszul and Ringel duality in terms of a weight
complex functor and show that partial quiver flag varieties in affine type A
(with cyclic orientation) admit an affine paving.
