Inspired by the emerging Big Data challenge, in this paper we provide the description of OLAP*, a Cloud-based framework for supporting effective and efficient OLAP in Big Data environments. OLAP* combines data warehouse partitioning techniques with Cloud Computing paradigms, and provides a suitable implementation on top of the well-known ROLAP server Mondrian where the main task consists in applying meaningful transformation of multidimensional database schemas. We complement our analytical contribution by mean of a case study showing the effectiveness of our framework in a practical setting.