I removed the fuel cap from a K100 that had been neglected for many years. 
The screws that secured the cap to the tank did NOT come out! There is NO head on the screws anymore.

How am I going to re-attach a cap to this tank? What would you do?

I'd find some way to unscrew the studs remaining from the screws and replace the screws with new ones. There looks to be parts of the screw shank above the base.  Easy to grab with pliers.  Any reason you haven't tried this?

Because the cap assembly screws have been that way since last September, it's clear there is no lack of patience at your end with this project.   I'd spray the screw stubs with Liquid Wrench, let it penetrate for 10 minutes or so, then attempt what robmack has suggested or attempt to remove them from below if they protrude.

There are other options such as drilling out the old screws and tapping for new screws, or drilling and tapping new holes near the old holes, but safe procedure demands gasoline fumes must be eliminated first.

If you're going to use penetrating oil then let it sit overnight or however long it recommends on the can.

strip the internals of the tank  , grind the studs flat , centre studs and drill out . this is a common problem , or rotate cap and drill tank for new fixings or have the alloy monza type cap welded in place ( last resort ) because in a front end crash this cap will rip your balls off   one of the reasons they stopped using them in the 1960s on british bikes .

firstle wrote:strip the internals of the tank  , grind the studs flat , centre studs and drill out . this is a common problem , or rotate cap and drill tank for new fixings or have the alloy monza type cap welded in place ( last resort ) because in a front end crash this cap will rip your balls off   one of the reasons they stopped using them in the 1960s on british bikes .

How do you change the fuel filter or address fuel pump issues with a welded on gas cap?

I would drill and tap holes at 45 degrees from the old holes. Do it through the base of the gas cap with it in place to ensure hole alignment between the gas cap and tank.

Hot air gun to warm aluminium, tap small sharp screwdriver with a hammer to create a groove for the screwdriver to bite onto and wind the screws clockwise into the tank and catch them before they disappear into the depths.

Its an SE tank so its worth treading carefully. 

A week or more going at it with penetrating fluid is a good idea. Go way beyond the 10 minutes and it can make a difference. Use of modest heat by way of a hair dryer will warm it without damaging the paintwork, assuming the tank is devoid of any petrol fumes, get them warm as you can then penetrating oil into them, a little more gets drawn in each time. It will give you your best chance when you do eventually go at them. Patience is key and this is best done slowly.

duck wrote:

firstle wrote:strip the internals of the tank  , grind the studs flat , centre studs and drill out . this is a common problem , or rotate cap and drill tank for new fixings or have the alloy monza type cap welded in place ( last resort ) because in a front end crash this cap will rip your balls off   one of the reasons they stopped using them in the 1960s on british bikes .

How do you change the fuel filter or address fuel pump issues with a welded on gas cap?

I would drill and tap holes at 45 degrees from the old holes. Do it through the base of the gas cap with it in place to ensure hole alignment between the gas cap and tank.

this style of replacement enables you to place the fixings in another location and still have the cap opening the correct way , in line etc , or anyway you like , i would not like it my self as the filler sits above the tank and would be a nasty hazard . i have seen these used MOTONE BMW K75 K100 K1100 K SERIES AIRHEAD MONZA GAS FUEL PETROL TANK CAP KIT | eBay this is one fitted 1989 bmw K75 cafe racer scrambler | eBay

Penetrating oil left to soak for at least a week.  Apply daily along with some heat, followed by a sharp tap with a small hammer to break loose the corrosion. 

Don't use WD40.  WD40 is NOT penetrating oil.  I like Liquid Wrench.

You can also use nitric acid as it will eat the steel but not the aluminium. Just a tiny bit at a time on the rusty screw, it takes a while but I have had success in the past with it.

Thanks to everyone for the replies.

I chose to follow Duck's suggestion of drilling and tapping new holes, and grinding the old studs down. For a replacement, I bought a screw-top aluminum cap from ebay. I couldn't find any replacement caps with a hole for the drain. I guess it's not worth putting that hole in the gasket here.

I used a 1/8" drill bit and a drill press, using the old cap as a guide (Perhaps over-cautiously, I duct taped it secure to the tank. Sadly this removed a chip of paint from a scratch.) I used an M4-0.7 tap to match the screws that came with the cap.

The screws are 13 mm, and they go about 8 mm into the aluminum, so I tried to drill only so far into the tank.

Take out the aluminum mounting plate if it has one.

Get an easy out that is 1/2 the diameter of the broken off screws.  Buy a cobalt drill to suit.  Pay the money and get one made with a cobalt steel alloy.
Center pop the screw stub.  Set up you tank under a drill stand so the screw axis is in line with the drill axis.    Set the drill speed to as low as it will go.
Drill out the axis of the screw.

Carefully insert the easyout in a tap holder, an slowly and gently screw easy out into the hole in the screw buy gently turning the easy out counter clockwise until it locks In place.   Gently turn the easy out counter clockwise, while gently tapping the easy out shaft at the tap holder end.  Requires three hands.       If it does not move, get a good peneterting fluid, or if there is gasket goo used previously, put a couple of drops of acetone onto the screw wait 30seconds and try again.        

OR
FIND A GOOD ENGINEER/MECHANIC with a fully equipped workshop to do it.  Less stuffing around.