Group Activity Recognition (GAR) detects the activity performed by a group of actors in a short video clip. The task requires the compositional understanding of scene entities and relational reasoning between them. We approach GAR by modeling the video as a series of tokens that represent the multi-scale semantic concepts in the video. We propose COMPOSER, a Multiscale Transformer based architecture that performs attention-based reasoning over tokens at each scale and learns group activity compositionally. In addition, we only use the keypoint modality which reduces scene biases and improves the generalization ability of the model. We improve the multi-scale representations in COMPOSER by clustering the intermediate scale representations, while maintaining consistent cluster assignments between scales. Finally, we use techniques such as auxiliary prediction and novel data augmentations (e.g., Actor Dropout) to aid model training. We demonstrate the model's strength and interpretability on the challenging Volleyball dataset. COMPOSER achieves a new state-of-the-art 94.5% accuracy with the keypoint-only modality. COMPOSER outperforms the latest GAR methods that rely on RGB signals, and performs favorably compared against methods that exploit multiple modalities. Our code will be available.