  For any smooth algebraic curve C, Pavel Etingof introduced a `global'
Cherednik algebra as a natural deformation of the cross product of the algebra
of differential operators on C^n and the symmetric group. We provide a
construction of the global Cherednik algebra in terms of quantumn Hamiltonian
reduction. We study a category of character D-modules on a representation
scheme associated to C and define a Hamiltonian reduction functor from that
category to category O for the global Cherednik algebra.
  In the special case where the curve C is the multiplicative group, the global
Cherednik algebra reduces to the trigonometric Cherednik algebra of type A, and
our character D-modules become holonomic D-modules on GL_n \times C^n. The
corresponding perverse sheaves are reminiscent of (and include as special
cases) Lusztig's character sheaves.
