Why did the Germans send a expeditionary force to North Africa?

The Italians had taken a big thrashing in Libya from the British in Operation Compass during the Winter of 1940-41.They had lost 138,000 men as POws (out of a total force of 150,000),2/3 of their tanks,over half their guns,and 564 aircraft.Total British casualties were under 2000.

The Italians were in full retreat,and the potential loss of the whole of Libya was only prevented when the British government decided to send most of the Western Desert Force to Greece in mid February following the Italian invasion there October 1940 (a wholly unnecessary redeployment at the time,as the Greeks were more than holding their own against the Italians in early 1941).This meant the British had to halt their ongoing offensive in Libya.

Hitler saw no option other than to send German troops to North Africa to prop up Italian forces there,as it really did look as if the Italians might be forced out of Libya altogether at the time.

When?

In WW2 the German forces (Afrika Corps) took over in North Africa when the Italians were collapsing.

In WW1 Germany deplloyed small forces into Africa South of the Sahara. - the East Africa campaign was hard fought.

The German forces themselves didn't really want to intervene in Afrika, but Italy wanted to rebuild the Roman Empire and were having losses in North Africa, so Hitler set up a force to help the Italians this was what the Afrika Korps purpose was.

Oil had a lot to do with it. Since armies were mechanized during WWI, they needed fuel. Lots of oil in the middle east and North Africa is the doorway.

They wanted to take the Suez Canal. That would have cut off a vital supply line to Britain.

They initially intervened to shore up their Italian allies