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He is being tried in absentia because Washington has ruled out handing him over and his lawyer, Alberto Biffani, indicated his client could formally reject the Italian court's authority.
"Of course, Mr. Lozano will reject that this court has jurisdiction in this case," Biffani told reporters.
The U.S. and Italian governments said the shooting was an accident, but an Italian judge charged Lozano with murder and two counts of attempted murder of those in the car.
His trial began in a courtroom inside Rome's maximum security prison, Rebibbia, the largest in the Italian capital. Seven empty cages flanked the left side of the courtroom, normally used to hold high-security defendants.