Look up Operation Mincemeat. Essentially the British forged plans to jnvade Greece. Then, they took a homeless Welsh man's dead body, dressed him up with a false identity and officer's uniform and made sure he washed up in Occupied Europe where Hitler could see. Then they launched a huge covert operation to "recover" the plans (making certain Hitler would see them).

Hitler, believing himself a genius, orders many troops to Greece to prepare for said invasion. These troops then remain there because he thinks Sicily is "a diversion" (the same reason he kept divisoins in Calais when D-Day happened).