I encountered this sentence recently and it confounds me: "Warten Sie auf mich?" as in "Do you wait for me?". Since we have a two-way preposition and because there is no motion in this sentence, I was under the impression that it would be "Warten Sie auf mir?". Why don't we use the dative case here?
"Auf ... warten" (meaning "to wait for ...") takes always the accusative case in German. The dative case would indicate that you stand or sit somewhere while waiting, say, "Ich warte auf der Bank (dat.) auf dich (akk.)", meaning "I wait for you sitting on the bench".