  We establish an embedding of the quantum enveloping algebra of a symmetric
generalized Kac--Moody algebra into a localized Hall algebra of $\mathbb
Z_2$-graded complexes of representations of a quiver with (possible) loops. To
overcome difficulties resulting from the existence of infinite dimensional
projective objects, we consider the category of finitely-presented
representations and the category of $\mathbb Z_2$-graded complexes of
projectives with finite homology.
