No wireless

When you say, "does not accept", you mean your plug won't physically fit in the jack? Or something else.
 
The Luke has active electronics, which are on when anything is plugged in. Those can often cause issues with many wireless systems.
 
I use a Shure glxd system on all my EBMM’s with no issues.... all active as well. Granted, I don’t own a Luke...
 
Never had a problem with a Line6 G30 and Luke II (active electronics), IIIs have passive pickups. Suspect something else but it would help if the OP described the problem in detail.
 
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