The aim here is to make sure security is supporting the business objectives and strategy. Every department in the hybrid model in turn decides how their security efforts contribute to the overall risk reduction and better security posture.
A single function responsible for all aspects of a Cloud security: people, process, technology, governance, operations, etc. Strategic direction is set centrally, while all other capabilities are left up to existing teams to define. Strategy, policy, governance and vendors are managed by the Cloud security team; other capabilities remain outside the Cloud security initiative.