What to do!?!

OK, based on what you've told us, it seems that he is purposefully dragging the game out. I agree, that is not particularly sportsmanlike. I would not go so far as to call it immoral though! He is playing within the rules.

I do consider it to be unsavory, but it is really a minor thing.

I would say, however, that publicly criticizing someone, and making a big stink about it is worse.

Or are you too closed minded to consider that perhaps you are in the wrong?

Originally posted by GrebartsBocaj
When I started out playing OTB I once forgot to turn of my mobile phone and it rang. My opponent called after the arbiter and told him to forfeit the game for me. Surely this example followed the rules but was it really fair out of a wider perspective.

Yes.