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

Representation Theory;Combinatorics;Quantum Algebra