A quantum symmetric pair consists of a quantum group and its coideal subalgebra (called an $\imath$quantum group). A quantum group can be viewed as an example of $\imath$quantum groups associated to symmetric pairs of diagonal type.

Recently, we present a geometric construction of affine $\imath$quantum groups in Drinfeld type presentation. For simplicity, in this talk, we mainly focus on the $\imath$quantum group of type affine $\mathfrak{sl}_2$, which is also called $q$-Onsager algebra. The Drinfeld type presentation of the $q$-Onsager algebra is introduced, and it can be realized by using the $\imath$Hall algebra of the projective line.

This is joint work with Shiquan Ruan and Weiqiang Wang.