  We introduce an elliptic version of the Grothendieck-Springer sheaf and
establish elliptic analogues of the basic results of Springer theory. From a
geometric perspective, our constructions specialize geometric Eisenstein series
to the resolution of degree zero, semistable G-bundles by degree zero B-bundles
over an elliptic curve E. From a representation theory perspective, they
produce a full embedding of representations of the elliptic or double affine
Weyl group into perverse sheaves with nilpotent characteristic variety on the
moduli of G-bundles over E. The resulting objects are principal series examples
of elliptic character sheaves, objects expected to play the role of character
sheaves for loop groups.
