In the Numenera Corebook, rules for expending XP (p112 in particular) state that one can spend 3 XP to obtain a long-term benefit, in particular to craft an artifact:
Artifact: The PC creates an artifact that has a power of his choosing. If the item is fairly simple, the GM can skip the crafting details and just say that after a period of time, the PC creates it. For an item that significantly alters gameplay—granting the character vast telepathic powers or giving him the ability to teleport at will—the GM might require difficult rolls, a considerable amount of time, and rare, hard-to-find components and materials
On the other hand, a few pages earlier (p109), the corebook states that when players find or are given an artifact, they should be awarded XP equal to the artifact level (minimum 1XP per player):
Artifacts: When the group gains an artifact, award XP equal to the artifact’s level and divide it among the PCs (minimum 1 XP for each character). Round down if necessary. For example, if four PCs discover a level 5 artifact, they each get 1 XP.
Now, one of my players chose the "Crafts Unique Objects" focus, and has told me he's very interested in crafting "a motorcycle". This would have to be an artifact, as I see it. It would take him some time to craft, and be difficult, since he's tier 1. But my question is about the interaction of these two rules. Should I take the 3 XP from him and then pass the resulting XP to the group? Should it work some other way? I didn't see anything in the focus (for tier 1) that would contradict this.