  We provide a direct proof of Seidel representation in the quantum K-theory
QK(Gr(k, n)) by studying projected Gromov-Witten varieties concretely. As
applications, we give an alternative proof of the K-theoretic quantum Pieri
rule by Buch and Mihalcea, reduce certain quantum Schubert structure constants
of higher degree to classical Littlewood-Richardson coefficients for K(Gr(k,
n)), and provide a quantum Littlewood-Richardson rule for QK(Gr(3, n)).
