There are many works on geometric representation theory of quiver varieties and their relation to quantum loop algebras and Yangians. Recently, I have been interested in their variants, where quiver varieties are replaced by σ-quiver varieties, the fixed point loci of involutions on quiver varieties. I will explain my recent work on geometric representation theory of σ-quiver varieties and twisted Yangian, focusing on the special case of cotangent bundles of l-step isotropic flag varieties.