When someon says "το δικό μου..." in Greek, the emphasis is given on the actual possession.
To make it a bit more clear:
Someone asks you what are you doing right now. You'd reply with "I'm eating my sandwich - Τρώω το σάντουιτς μου."
Someone accuses you of eating their sandwich. You'd reply with "I'm eating my own sandwich - Τρώω το δικό μου σάντουιτς."
No, how? It doesn't end in one of the standard declension endings :)
A fair number of loanwords are not inflectible because they don't fit the "shape" of Greek words.
(Old loanwords tended to be assimilated, often by adding -ι, in order to make them inflectible. But modern ones are often borrowed as-is.)