Cloud computing is clearly one of today's most dominant paradigms in the Information Technology (IT) industry due to its scalable, flexible, and cost-efficient access to infrastructure and application services. Despite these promising facilities and benefits, cloud users have serious concerns about the data security and privacy. Among all security challenges, access control is of vital importance, since it provides security mechanisms to protect customer's data, cloud services, applications, resources against unauthorized access, and misuse of privileges. Several access control systems have been proposed in literature lately but most of them are designed to work with one specific access control policy. In this paper, we present a novel generic access control scheme, capable to work with most of the available access control policies using a global resource management system (GRMS) to effectively handle both local and remote authentication requests. The introduction of GRMS makes our proposed architecture semi-distributed at the expense of minimal request-response time. We have shown the applicability of our proposed architecture using a case study for three different scenarios.