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"We introduce an affine Schur algebra via the affine Hecke algebra associated to Weyl group of affine type C. We establish multiplication formulas on the affine Hecke algebra and affine Schur algebra. Then we construct monomial bases and canonical bases for the affine Schur algebra. The multiplication formula allows us to establish a stabilization property of the family of affine Schur algebras that leads to the modified version of an algebra Kc n. We show that Kc n is a coideal subalgebra of quantum affine algebra Uppglnq, and Uppglnq,Kc nq forms a quantum symmetric pair. The modified coideal subalgebra is shown to admit monomial and stably canonical bases. We also formulate several variants of the affine Schur algebra and the (modified) coideal subalgebra above, as well as their monomial and canonical bases. This work provides a new and algebraic approach which complements and sheds new light on our previous geometric approach on the subject. In the appendix by four of the authors, new length formulas for the Weyl groups of affine classical types are obtained in a symmetrized fashion"--

Hecke algebras. --- Schur complement. --- Affine algebraic groups. --- Quantum groups. --- Nonassociative rings and algebras -- Lie algebras and Lie superalgebras -- Representations, algebraic theory (weights). --- Group theory and generalizations -- Linear algebraic groups and related topics -- Quantum groups (quantized function algebras) and their representations. --- Group theory and generalizations -- Linear algebraic groups and related topics -- Schur and $q$-Schur algebras.