How to type keyboard shortcuts like ⌘Ä, ⌘Ö, ⌘Ü, etc. on a US keyboard? I'm using a Mac laptop with German set as the preferred language (the keyboard, however, is a standard US keyboard).  With this setting, some keyboard shortcuts include the characters Ä, Ö, and Ü.  E.g. ⌘Ä (command-Ä), ⌘Ö (command-Ö), ⌘Ü (command-Ü), etc.

Now, I produce Ä by first pressing ⌥-u (Option-u), and then pressing ⇧-a (Shift-a).  I can't figure out any way of using this method to produce the equivalent of ⌘Ä (command-Ä).  The same goes for for Ö and Ü.

Is there some way to produce these keyboard shortcuts on a US keyboard?
This may seem metaphysical, but you cannot press a key that does not exist. Despite the lack of a physical Ä key on the U.S. Keyboard, you can, however set the keyboard layout to the German keyboard layout. Alternately, you could create a modified keyboard layout starting from the standard U.S. Keyboard layout that includes a Ä key.

The operation of changing the layout is the simplest to accomplish:


Go to System Preferences » Language &amp; Text » Input Sources 
Enable the German layout (and also make sure the "Show Input menu in menu bar" box is checked).
In the Input menu, select the German layout. 


Then, pressing the physical ⌘' keys will produce the ⌘Ä sequence. Likewise for ⌘; producing ⌘Ö and ⌘[ producing ⌘Ü. After typing that keystroke, you can use the menu to switch back to your desired keyboard layout.