  The $\imath$quiver algebras were introduced recently by the authors to
provide a Hall algebra realization of universal $\imath$quantum groups, which
is a generalization of Bridgeland's Hall algebra construction for (Drinfeld
doubles of) quantum groups; here an $\imath$quantum group and a corresponding
Drinfeld-Jimbo quantum group form a quantum symmetric pair. In this paper, the
Dynkin $\imath$quiver algebras are shown to arise as new examples of singular
Nakajima-Keller-Scherotzke categories. Then we provide a geometric construction
of the universal $\imath$quantum groups and their ``dual canonical bases" with
positivity, via the quantum Grothendieck rings of Nakajima-Keller-Scherotzke
quiver varieties, generalizing Qin's geometric realization of quantum groups of
type ADE.
