I'm not absolutely certain what the best construction would be for the example you gave. I think you can use á½¡Ï‚ the way you did, although it isn't the most common use. Ï†á½»Î»Î±ÎºÎ±Ï‚ should be in the same case as its antecedent.
There's also another way in Greek to express a noun which is in apposition with another noun. This is where the Attic use of the article becomes quite useful. In the nominative you would write Î¿á¼± Î˜Ïá¾·ÎºÎµÏ‚ Ï†á½»Î»Î±ÎºÎµÏ‚ (Îµá¼°ÏƒÎ¹Î½); the noun with the article is the subject, the one without is the predicate. With verbs of naming and the like (where it's natural to have a noun or adjective in apposition with the direct object) you can do the same thing: á¼Îºá½±Î»ÎµÏƒÎµ Ï„á½¸Î½ Î£Ï‰ÎºÏá½±Ï„Î·Î½ ÏƒÎ¿Ï†á½¹Î½
I'm not sure whether you could say Ï†á½»Î»Î±ÎºÎ±Ï‚ á¼”Ï€ÎµÎ¼ÏˆÎµ Ï„Î¿á½ºÏ‚ Î˜Ïá¾·ÎºÎ±Ï‚, however. It doesn't sound quite right for some reason and I can't find the section in my grammar at the moment which talks about this (apart from verbs which normally take a double accusative)
IPHIGENIE: Kann uns zum Vaterland die Fremde werden?
ARKAS: Und dir ist fremd das Vaterland geworden.
IPHIGENIE: Das ist's, warum mein blutend Herz nicht heilt.
(Goethe, Iphigenie auf Tauris)