Nowadays, one of the main research issues of great interest is the efficient tracking of mobile objects that enables the effective answering of spatiotemporal queries. This line of research is relevant to a number of modern applications spanning many contexts. In this paper, we consider the organization of a moving object database by quadtree based structures (structures obeying the Embedding Space Hierarchy). In this context, we adapt an indexing method, called XBR trees, to support range queries about the history of trajectories of moving objects. The XBR tree is a quadtree like external memory, balanced and compact structure that follows regular decomposition. Apart from the presentation of the new method, we experimentally show that it outperforms the only previous Embedding Space Hierarchy approach (based on PRM quadtrees) for indexing moving objects.