You can move global objects within or between the Browser tree view and the diagram window.
Select to make sure that Move is the Default action of the Drag & Drop option.
You can move a global object within the Browser to convert it into a local object (under a group particle item), but you cannot move a global object within its own structure (as a child of itself).
You can move a global object within the diagram to convert it into a local object. Just move the global object symbol to a group particle symbol.
When you move a global object from the Browser to the diagram, a synonym symbol is created in the diagram.
You can move a global object from the diagram to the Browser, and convert it into a local object (under a group particle item). If the new local object does not appear in the diagram, double-click the Collapse node of the group particle symbol under which the former global object has been attached.