This article presents a novel multi-agent spatial transformer (MAST) for learning communication policies in large-scale decentralized and collaborative multi-robot systems (DC-MRS). Challenges in collaboration in DC-MRS arise from: (i) partial observable states as robots make only localized perception, (ii) limited communication range with no central server, and (iii) independent execution of actions. The robots need to optimize a common task-specific objective, which, under the restricted setting, must be done using a communication policy that exhibits the desired collaborative behavior. The proposed MAST is a decentralized transformer architecture that learns communication policies to compute abstract information to be shared with other agents and processes the received information with the robot's own observations. The MAST extends the standard transformer with new positional encoding strategies and attention operations that employ windowing to limit the receptive field for MRS. These are designed for local computation, shift-equivariance, and permutation equivariance, making it a promising approach for DC-MRS. We demonstrate the efficacy of MAST on decentralized assignment and navigation (DAN) and decentralized coverage control. Efficiently trained using imitation learning in a centralized setting, the decentralized MAST policy is robust to communication delays, scales to large teams, and performs better than the baselines and other learning-based approaches.