The US DID do something similar - a fake army:
Really fun and informative. The army recruited artists to design phony inflatable tanks and the like...
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One of the many fun facts I picked up from Paul Harvey’s “The Rest of the Story”: The fashion designer Bill Blass was one of the artists that helped create many of the facades used in this great military diversion.
The fake paratroopers are the best. Jerry had to no choice but to run a unit out to see if they were real or not. There is some Nazi film at the WWII museum in New Orleans, which by the way is top notch.