  Equivariant map algebras are Lie algebras of algebraic maps from a scheme (or
algebraic variety) to a target finite-dimensional Lie algebra (in the case of
the current paper, we assume the latter is a simple Lie algebra) that are
equivariant with respect to the action of a finite group. In the first part of
this paper, we define global Weyl modules for equivariant map algebras
satisfying a mild assumption. We then identify a commutative algebra A that
acts naturally on the global Weyl modules, which leads to a Weyl functor from
the category of A-modules to the category of modules for the equivariant map
algebra in question. These definitions extend the ones previously given for
generalized current algebras (i.e. untwisted map algebras) and twisted loop
algebras.
  In the second part of the paper, we restrict our attention to equivariant map
algebras where the group involved is abelian, acts on the target Lie algebra by
diagram automorphisms, and freely on (the set of rational points of) the
scheme. Under these additional assumptions, we prove that A is finitely
generated and the global Weyl module is a finitely generated A-module. We also
define local Weyl modules via the Weyl functor and prove that these coincide
with the local Weyl modules defined directly in a previous paper. Finally, we
show that A is the algebra of coinvariants of the analogous algebra in the
untwisted case.
