AirAsia India, a joint venture between Tatas and Malaysia's AirAsia Berhad, flies to 11 destinations.
The airline recently came into focus after ousted Tata Sons Chairman Cyrus Mistry alleged fraudulent transactions worth Rs 22 crore took place at the carrier.
The airline today said the decision was taken at its board meeting held on November 29.
"I would like to congratulate Amar on being unanimously chosen by the AirAsia India Board to become the MD in addition to his current role as the CEO.
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Abrol, who has over two decades of experience in different markets including Hong Kong, Singapore, the UK and Malaysia, was appointed as CEO in April 2016.
At the end of October, AirAsia India had a market share of 2.7 per cent and carried 2.36 lakh passengers that month.
Last month, Abrol told PTI that the airline would continue to make investments and expand fleet size to 10 in the current financial year. It has eight aircraft.
Following Mistry's allegation, AirAsia India, on October 31, had said that probe is going on against certain former executives for "irregular personal expense claims" and other charges.
In the airline, Tata Sons owns 49 per cent while two of the airline's directors -- S Ramadorai and R Venkataramanan -- have 2 per cent shareholding, and the remaining is with AirAsia Berhad.
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