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Batter Shimron Hetmyer, who was dropped from the West Indies squad for the previous T20 World Cup after missing his flight to Australia, was also called up by the twice champions.
He will join LSG for Rs 3 crore and this will be Joseph's first stint in the IPL.
Paceman Joseph's incredible seven-wicket haul in the second innings of the eight-run upset at the Gabba on Sunday came after he was forced to retire hurt due to a toe-crushing Mitchell Starc yorker the previous evening.