  In this paper, we introduce a multidimensional generalization of Kitagawa's
split-step discrete-time quantum walk, study the spectrum of its evolution
operator for the case of one defect coins, and prove localization of the walk.
Using a spectral mapping theorem, we can reduce the spectral analysis of the
evolution operator to that of a discrete Schr\"{o}dinger operator with variable
coefficients, which is analyzed using the Feshbach map.
