Learn Turkish: İradem güçlü olduğu halde hamur işi yiyorum. - Even though my willpower is strong, I eat pastry.

The concessive clause ('even though my willpower is strong') has its own subject. The subject here is iradem (my willpower), which is a third-person entity ('it'). Therefore, the participle takes the third-person possessive suffix -u, becoming olduğu. The main verb yiyorum takes the first-person suffix because 'I' am the subject of the eating action.

What does halde actually mean in this grammar structure?

The word hal means 'state' or 'situation', and the -de is the locative suffix meaning 'in' or 'at'. So, olduğu halde literally translates to 'in the state of its being'. Turkish uses this phrase to express 'even though' or 'despite the fact that'.

Why doesn't hamur işi take an accusative ending since it is the direct object?

Hamur işi is a noun compound literally meaning 'dough work' (used for pastry or baked goods). It remains in its bare form here because it is a non-specific object. You are saying 'I eat pastry' in general, rather than 'I am eating the pastry', which would require the accusative case.

How did the participle olduk turn into olduğu?