At present the kitchen sink, drain pipe runs through the centre of the existing lower cupboards to the stack ( our home was built in 1915, therefore the stack is original) we are replacing these lower cupboards, and would like to know how to reroute the drain to the stack without having to run them through the middle of the new cupboards?

Do you have any space below the kitchen, such as a basement or crawl space, such that you can route the drain straight down from the sink, then tie into the stack down below?

Unless you're talking about the vent stack which goes out the roof? In that case, I know one option for things like kitchen islands is to vent the drain pipe directly into the cupboard space below the sink. You have to install a special check valve which allows air to be sucked into the vent as a vacuum break when water is flowing, but doesn't allow sewer gases to flow back out when the water stops.

Best is going straight down and below the floor and joining the stack in the basement.
Or opening the wall and cutting 1 1/2" holes in the studs, something you want to avoid in a bearing wall.
Or.. you could run under the 4" kickbase of the new cabinets, as long as you have the slope needed, and realize that it's going to be inaccessible.

Weird... I edited this answer in the old skin after I realized the OP meant the sewer stack. The edit shows up in the old skin, but not the new "Go" skin.

If no access under the floor, and no fixtures dump into the stack above where the kitchen sink ties in, then I would suggest opening the wall and drilling the studs with a 2 9/16 bit at a 1/4 inch per foot slope. Even on a load bearing outside 3 1/2 wall, this is acceptable in almost all areas as the outside sheeting reinforces the wall anyway. We do it here all the time, and I know other plumbers in all different areas that do also. This would be your best option. Just remember to use stud gaurds to protect the pipe from screws when the sheetrock is put back up.