BMW makes a hard and soft topcase of about 21 litres and Givi makes an assortment of sizes. I use the BMW hardcase and have been well pleased with it although one or two have reported the case coming loose. If you search the archives (try 'BMW topcase') you will find much more info and pictures.
When looking at this question on another board someone mentioned the Givi E30N top case. They even showed some photos on their K12GT, and it looked O.K. because it was a smaller case. Plus they are only about $85 mail order, and supposedly their base mounts directly to the luggage rack of the K12GT (although you might need to get some longer SS bolts).
If looking for a hard case this was definitely something that I was going to try.
Givi 46 liter case for me. Not too big, not too small. Holds 18 bottles of beer, a twelve pack of diet coke (cans) a liter of Diet Coke and over ten pounds of ice at the same time (I was thristy at Laguna Seca).
A forum community dedicated to BMW K series motorcycles owners and enthusiasts. Come join the discussion about performance, touring, gear, modifications, classifieds, troubleshooting, maintenance, and more!