  We construct the first measure-preserving affine actions with spectral gap on
surfaces of arbitrary genus $g > 1$. We achieve this by finding geometric
representatives of multi-twists on origami surfaces. As a major application, we
construct new expanders that are coarsely distinct from the classical expanders
obtained via the Laplacian as Cayley graphs of finite quotients of a group. Our
methods also show that the Margulis expander, and hence the Gabber--Galil
expander, is coarsely distinct from the Selberg expander.
