Categorification of quantum symmetric pairs I

We categorify a coideal subalgebra of the quantum group of sl(2r+1) by introducing a 2-category analogous to the one defined by Khovanov-Lauda-Rouquier, and show that self-dual indecomposable 1-morphisms categorify the canonical basis of this algebra. This allows us to define a categorical action of this coideal algebra on the categories of modules over cohomology rings of partial flag varieties and on the category O of type B/C.