KAP140 Autopilot Details

I have a question about some nuances of the Bendix/King KAP 140 autopilot.
Since the ink is still wet on my IFR rating (actually I have not even gotten
the new one in the mail yet!) I am working on a personal "post checkride"
syllabus. Part of this self training is to fly different routes on an IFR
clearance in VMC using the autopilot. In all my VFR days I never touched
the thing and was not allowed to use it during my IFR training. While I am
serious about keeping my hand flying skills sharp, I also want to know how
to use the autopilot. After reading the manufacturer's "Pilot's Guide"
cover to cover I noticed a rather odd procedure when using the AP in
conjunction with a DG. When you select NAV the AP temporarily flashes HDG
to remind you to set the Heading Bug to the same course as set on the OBS.
I do this and everything works fine but I want to understand WHY you do
this. What algorithm is the autopilot is using? How does it uses the
Heading bug info in conjunction with the OBS and CDI? I noticed that once I
am tracking a radial if I change the HDG bug the aircraft turns. My mental
model has the autopilot just using the CDI deflection and OBS setting to
hold a course, but obviously I am missing something. If anyone can point me
to some more detailed information on how the AP uses the Heading Bug while
in NAV or APR mode I would appreciate it.

thanks
Martin Van Ryswyk
PPSEL Instrument