I want to do something for someone, but also want to express that i don´t expect anything in return, and that she should not feel any obligation whatsoever.

What turkish words could best be used to describe that?

 Can´t you be a bit more concrete? This is kind of vague. All that I can come up with is ihsan etmek (to bestow a favour) or iyilik etmek/yapmak (to do kind, a favour), but that does not fully cover what you want to say I suppose.

If you are close to this person, you can use this expression.  I say close, because you don´t say it to a person you just met.  But it exactly means, you want to do a favour and do not want anything in return:

Kıyak çekmek is the verb form..  Sana

If you want to express that you do not expect anything back, you can say afterwards your favor, "içimden geldi" forexample you give someone a present when it´s not a special day, you say "içimden geldi, aldım"

and the translation of "I do not expect anything in return" is "karşılık beklemiyorum"

Thank you, Merih and Mltm for answering my question despite the vagueness of it!

But you understood exactly what i was looking for!