Can anyone explain me please how to translate for example "aktardığımız, or  çevirdiği"

I don´t understand how does that yumuşak ğ appears and what role does it play in the word. Please help

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Why K becomes Ğ is explained here: http://www.turkishclass.com/turkish_lesson_63

As for meaning of both words - as far as I know, this form is called "object participle". You can find more about it here: http://turkishlanguage.co.uk/objectpart.htm

Sorry for not explaining it here myself, but being learner myself, I don´t feel confident enough :| Hope above links will help you.

It is DIK.

DIK is the subordinating suffix used in verbs. There are no subclauses in Turkish like in English. In the corresponding constructions verbs are usually subordinated with DIK. Words marked with DIK are not finite verbs any more but more like adjectives and they do not take personal endings but possessive suffixes. Their exact translation depends on their surroundings but you can always try with different kinds of English subclauses: çevirdiği ´that/which/from which/in which...he translates/translated/has translated´. As a single word DIK participle is very ambiguous, I would rather look at it always as a part of a sentence.

Every letter in DIK is subject to phonetical changes;

                          D can appear as d or t

                          I can appear as ı, i, u or ü

                          K can appear as k or ğ.

You will soon get used to it.