How do I connect the #6 Al wiring from my 40 amp breaker to the #8 Cu wires in my new cooktop?
Aluminum is common in this larger wire, and often, connections are made to screw-down lugs. In fact the lugs are often made of aluminum.  

So first, check the lugs on the range and see if they're already listed for aluminum.  If not, it may be possible to get lugs that are. 

Alternatively, you can get a wide variety of screw-lug splices for aluminum.  That's all an Alumiconn is - an exceptionally small lug.  The above link explains why they work.   This type of screw lug is also the standard wiring method in Europe.  Here are photos of Alumiconn; a larger lug connector (see the resemblance), and the Euro style.   Lastly, here's the split bolt that ThreePhaseEel is referring to. 






But the best way to please the Ms. is make sure you have a separate ground wire.  35 years ago, the common practice was to not bother running an equipment safety ground, and simply hijack neutral as ground. This is still permitted in old-work because of lobbying by appliance makers. But it's a terrible idea; if the neutral wire has a problem, the 120V loads in your range pull neutral up to 120V - and since neutral is tied to ground, this energizes the chassis of the machine at 120V.  Touch the range and the sink, and you're dead.   The good news is it's totally legal to retrofit just a ground wire and keep the conductors.