Which discard pile for instant items played on another player's lane?
I found the answer in the official FAQ (not included in the box published by EDGE) published on CMON website (game creator) : https://cmon.com/product/xenoshyft/xenoshyft-onslaught


  Q: If I play an Instant on another player’s lane (such as a Med
  Pack or Hi-Ex Grenade), does that card go to their discard
  pile?
  A: No, it goes to its owner’s discard pile. The only time a card
  goes to another player is if it is deployed into their lane.


Keeping Instant Cards played on someone else's lane in one's own discard pile allows us to better "build" around Division Cards abilities (such as "Whenever you play a [Symbol] card, heal 1 troop up to 2").