  Various constructions for quantum groups have been generalized to
$\imath$-quantum groups. Such generalization is called $\imath$-program. In
this paper, we fill one of parts in the $\imath$-program. Namely, we provide an
equivariant K-theory approach to $\imath$-quantum groups associated to the
Satake diagram in \eqref{eq1}, which is the Langlands dual picture of that
constructed in \cite{BKLW14}, where a geometric realization of the
$\imath$-quantum group is provided by using perverse sheaves. As an application
of the main results, we prove Li's conjecture \cite{L18} for the special cases
with the satake diagram in \eqref{eq1}.

Representation Theory