
abstellen
to turn off
To switch off a device, engine, or machine, or take it out of operation.
Vergiss nicht, den Motor abzustellen, wenn du parkst.
Don't forget to turn off the engine when you park.
to turn off / put down
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to turn off
To switch off a device, engine, or machine, or take it out of operation.
Vergiss nicht, den Motor abzustellen, wenn du parkst.
Don't forget to turn off the engine when you park.

to put down
To put or set an object down in a specific place.
Du kannst deine Tasche einfach hier in der Ecke abstellen.
You can simply put your bag down here in the corner.

to stop
To end or put a stop to unwanted behavior or an undesirable situation.
Wir müssen dieses unfaire Verhalten sofort abstellen.
We have to stop this unfair behavior immediately.

to assign
To assign or detach a person for a specific task or service.
Für die Nachtwache wurden zwei Soldaten abgestellt.
Two soldiers were assigned to night watch.

to focus on
To base something on a particular foundation or to be oriented toward something. Mostly used in formal or legal language.
Die Kritik stellt vor allem auf die mangelnde Transparenz des Verfahrens ab.
The criticism focuses primarily on the lack of transparency in the procedure.
'Abstellen' is a separable verb. In a main clause, the prefix 'ab-' stands at the end of the sentence. In a subordinate clause or with an infinitive with 'zu', the verb is not separated.
Stell bitte die Musik leiser oder ganz ab.
Please turn the music down or off completely.
The object of the verb reveals the meaning. You 'abstellen' devices (engine, light) in order to turn them off. You 'abstellen' objects (bag, bicycle) in order to put them down. You 'abstellen' problems (undesirable situation, behavior) in order to end them.
Er hat sein Auto direkt vor der Einfahrt abgestellt.
He parked his car right in front of the driveway.
In the meaning 'ausschalten' (to switch off), 'abstellen' is often used with technical devices or supply lines. Typical phrases are: 'den Motor abstellen' (to turn off the engine), 'das Licht abstellen' (to turn off the light), 'das Wasser abstellen' (to turn off the water), or 'den Strom abstellen' (to cut off the electricity).
Wegen der Reparatur müssen wir das Wasser für eine Stunde abstellen.
Because of the repair, we have to turn off the water for an hour.
In an abstract, often formal meaning, 'abstellen' is used for negative things that you want to end. For example, you can 'einen Missstand abstellen' (put an end to an undesirable situation), 'einen Mangel abstellen' (remedy a defect), or 'schlechtes Benehmen abstellen' (stop bad behavior).
Die Geschäftsführung versprach, die Mängel in der Produktion abzustellen.
Management promised to remedy the defects in production.
In the meaning 'basieren auf' (to be based on), 'abstellen' is fixed with the preposition 'auf' and the accusative. This construction is typical of administrative or legal language.
Das Urteil stellt auf die Aussagen mehrerer Zeugen ab.
The judgment is based on the statements of several witnesses.
to put / to set
Stellen and abstellen can both mean bringing an object to a specific place. Stellen describes general placement in an upright position; abstellen additionally emphasizes that the object is left there temporarily or will not be used further. Use stellen for a neutral movement and abstellen when emphasizing that something is being left there.

Ich stelle den Koffer neben dem Schrank ab, bis wir weiterfahren.
I put the suitcase down beside the cabinet until we set off again.
Ich stelle den Koffer neben den Schrank.
I put the suitcase beside the cabinet.