斡

A phono-semantic compound consisting of:

斗 (dipper; ladle) — semantic component; 倝 (gàn) — phonetic component, providing the sound. The original sense is linked to the handle of a ladle or scoop, an object that is turned or rotated in use. From this image, the meaning developed into: - physical rotation; - figurative “turning” of situations → managing or directing.
Semantic development: - handle of a ladle; - turning or rotating motion; - guiding or steering movement; - managing or mediating affairs. Thus, 斡 evolved from physical turning to abstract control and coordination.

간알 (斡旋) — mediation; arbitration

알선 (斡旋) — mediation; arrangement

The compound 斡旋 is the most common modern usage across Chinese, Korean, and Japanese. The reading 오 (o) appears in place names, while 알 (al) is used in general vocabulary. The shift from a physical tool (ladle handle) to abstract meanings highlights how manual action becomes metaphor for control and influence.
Related characters: 旋 — to rotate; to turn

轉 — to turn; to revolve

管 — to manage; to control

調 — to coordinate; to arrange

Among these, 斡 uniquely emphasizes active intervention or mediation, as if “turning the course” of events.