It should be executed on the retail market via a broker in the same way that you and I buy shares.
MM's literally make the markets that we buy and sell on: they are forced to buy when everyone is selling and sell when everyone is buying. A buyback on the exchange would execute at whatever the ask price was at the time and then the shares purchased would be reclassified as treasury shares.
MM's would position themselves accordingly to profit on the halves.
It would be a series of very large purchases extended out over several days or weeks, even months; probably 100 to 200 trades of 50mil or 25mil each.