  We generalize the geometric construction of quiver Hecke algebras from
Varagnolo and Vasserot to a setup with arbitrary connected reductive groups.
This corresponds to replacing quiver representations by generalized quiver
representations introduced by Derksen and Weyman. The class of algebras which
we construct contains (affine) nil Hecke algebras, skew group rings of Weyl
groups with polynomial rings and quiver Hecke algebras. We describe an explicit
faithful representation in a polynomial ring and we calculate the generators
and relations for these algebras.
