How to move a complex object to the origin without destroying it? I have a complex object far away from the origin of the scene itself.

If I mark all parts and use the Geometry to Origin function, the complex object gets crumbled, because all parts are set at the origin and the relations are destroyed.

Is there a way to move the object as a whole?

The object was an import from an STL file.
Go into edit mode, select all and press Shift-S and Cursor to selected. 

Then go back to object mode, press Ctrl-Alt-Shift-C, Origin to cursor, and then press Alt-G (clear location).