If you're in a fireteam with other people playing as different classes you get rep from their kills as well.
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With weapons, not with classes. I had no warlock kills, when all my friends were warlocks
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I never play as a hunter or warlock in crucible, I play with my friends who are those classes and they racked up the kills for me, possibly they fixed this but I was lucky enough have this happen for me.
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I had a titan..