Accelerometric gait identification systems should ideally be robust to changes in device orientation from the enrollment phase to the deployment phase. However, traditional Convolutional Neural Networks (CNNs) used in these systems compensate poorly for such distributional shifts. In this paper, we target this problem by introducing an SO(3)-equivariant quaternion convolutional kernel inside the CNN. Our architecture (Quaternion CNN) significantly outperforms a traditional CNN in a multi-user gait classification setting. Additionally, the kernels learned by QCNN can be visualized as basis-independent trajectory fragments in Euclidean space, a novel mode of feature visualization and extraction.