Hours after a battle in eastern Ukraine in August, a wounded and unarmed Russian soldier crawled through a nearly destroyed trench, seeking help from his captors, a unit of international volunteers led by an American.

The shooting of the unarmed, wounded Russian soldier is one of several killings that have unsettled the Chosen Company, one of the best-known units of international troops fighting on behalf of Ukraine.

In a second episode, a Chosen member lobbed a grenade at and killed a surrendering Russian soldier who had his hands raised, video footage reviewed by The Times shows.

In a third episode, Chosen members boasted in a group chat about killing Russian prisoners of war during a mission in October, text messages show.

A Greek soldier known as Zeus was at the center of all three episodes — tossing the grenade and, Mr. Grosse says, firing at the wounded Russian in the trench and bragging about another kill.

But in the United States military, a video showing the killing of a surrendering soldier, regardless of the circumstances, would prompt an immediate investigation, said Rachel E. VanLandingham, a professor at Southwestern Law School and a former U.S. Air Force lawyer.

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