we investigate the asymptotic structure of (possibly type iii) crossed product von neumann algebras arising from arbitrary actions of bi-exact discrete groups (e.g. free groups) on amenable von neumann algebras. we particularly prove a spectral gap rigidity result for the crossed products and, using recent results of boutonnet-ioana-salehi golsefidy, we provide the first example of group measure space type iii factors with no central sequences. this is joint work with c. houdayer.