The paper introduces Fourier Transporter (FOURTRAN), an open-loop behavior cloning method designed to improve sample efficiency in robotic manipulation tasks, particularly in 3D environments. FOURTRAN leverages the bi-equivariance symmetry in pick-place problems, where the distribution of actions transforms symmetrically when transformations are applied independently to the pick or place pose. The method uses a fiber space Fourier transformation to enable memory-efficient computation and high angular resolution. Tests on the RLbench benchmark show that FOURTRAN achieves state-of-the-art results across various tasks, outperforming existing methods by significant margins. The key contributions include a general theoretical solution for leveraging bi-equivariant symmetries and a practical implementation that demonstrates significant improvements in sample efficiency and success rates.The paper introduces Fourier Transporter (FOURTRAN), an open-loop behavior cloning method designed to improve sample efficiency in robotic manipulation tasks, particularly in 3D environments. FOURTRAN leverages the bi-equivariance symmetry in pick-place problems, where the distribution of actions transforms symmetrically when transformations are applied independently to the pick or place pose. The method uses a fiber space Fourier transformation to enable memory-efficient computation and high angular resolution. Tests on the RLbench benchmark show that FOURTRAN achieves state-of-the-art results across various tasks, outperforming existing methods by significant margins. The key contributions include a general theoretical solution for leveraging bi-equivariant symmetries and a practical implementation that demonstrates significant improvements in sample efficiency and success rates.