Re-reading on the problems of the Afrika Corps, regarding lack of equipment, while at the same time reading on early Barbarossa victories, a thought struck me: what if the german army had sent captured T-34s to Afrika Korps?
Bear with me for a moment. We know the germans used a lot of captured soviet equipment. Dozens of 76.2mm guns were used either as artillery or in Marder Jagpanzers, some of which also went to the AK. The use of captured T-34s is also on record. At the same time, there was the need to supply the AK with armour. And the T-34, with it's wide tracks and an operational range twice that of the PzIII or IV, would be ideal for the sandy/rocky wide areas of the desert.
So, instead of sending needed PzIII/IV, what if the germans send a new unit equiped with just T-34/76 from, say, November 1941? I don't think they could do it sooner. Say around 40-50 T-34s? Keep the PzIII/IV for the eastern front.
I realise this might be a problem, in terms of logistics, but that's nothing new. The efectiveness of the T-34 would, I think, overshadow those problems, since they were far superior to anything the british had.