Granting Permission To Security & Compliance, etc.

[Zeff Wheelock]

We have an on-premise Active Directory which we sync to the Office 365 cloud using Azure AD Connect.  We do not have a hybrid solution.  Is it possible to manage permissions to Security & Compliance center or as an Exchange Administrator or SharePoint Administrator from our on-premise Active Directory?  We have an Identity Manager tool which we manage all the users with.  Is it possible to manage Office 365 permissions and roles through on-premise AD?  

Or is it possible to create an AD group that could be put into the Exchange Admin role or any other security role that we can populate?  

The end-game here is the ability to manage administrative rights to Office 365 locally and have it sync to Office 365 through Azure AD Connect.  Any information on this would be appreciative.

[#2]

You need cloud identities to manage Office 365. You can create AD objects on-premises and sync them. After that, assign permissions to the synced cloud identity.

https://support.office.com/en-us/article/understanding-office-365-identity-and-azure-active-director...

[#3]

But can you create groups that can be managed by AD so you can add someone to the group that will grant them Exchange Administrator or Security & Compliance Administrator rights?