Hall algebras and quantum symmetric pairs of Kac-Moody type

We extend our $\mathrm{ı}$Hall algebra construction from acyclic to arbitrary $\mathrm{ı}$quivers, where the $\mathrm{ı}$quiver algebras are infinite-dimensional 1-Gorenstein in general. Then we establish an injective homomorphism from the universal $\mathrm{ı}$quantum group of Kac-Moody type arising from quantum symmetric pairs to the $\mathrm{ı}$Hall algebra associated to a virtually acyclic $\mathrm{ı}$quiver.