Unable to set user/group as principal on a proxy
A post for handling job permissions can be found at:

Allow non-sysadmin, non-owner of a SQL Server Agent job to execute it 

This post outlines:


Using standard SQL Agent roles such as SQLAgentOperatorRole.
 Note: Active Directory Groups are not able to login to start a job. 
Erland Sommarskog's post http://www.sommarskog.se/grantperm.html#countersignatures outlines using countersignatures.  This is a more complex setup, but it does work.
Points to a custom StartAgentJob stored procedure to allow rights to be granted within the context of the procedure.  This includes support of AD Groups as well.  The custom StartAgentJob has code in it that explicitly allows members of an Active Directory Group (but not the Active Directory Group itself) to start a job that they do not own.