Some of my friends use the word "грёбаный". Where does it come from? I suggested to myself that it could be somehow linked to words like "бан" or "баня", but it does not make sense in a sentence "Грёбаные кроссовки, почему они не налезают на ногу!?"
It's a euphemism of ёбаный ("fucking", literally "fucked"), same as in English "frigging" instead of "fucking".
The root itself is a descendant of a PIE root meaning "to dig, to scratch". This word is akin to гроб ("coffin"), English "grub", "grave" etc.
Word "гребаный" is a variation of "ебаный" that translated to English literally means "fucking". The origins of this word goes back to "Perestroyka" period in Soviet Union in the middle of the 80s. At the time with the freedom of expression came a whole new wave of cinema reflecting not "Soviet Realism", on which the entire SU population was raised, but the everyday struggle of younger generation who were disillusioned in the ideas of Socialism and leaned to Western ideology. One of the brightest example of this new direction in cinema was the movie "Маленькая Вера" ("The Little Vera") that was pretty explicit for its times. Now, in Russian language using cuss words is a taboo, be it a TV or literature or any kind of media. No amount of freedom of expression has ever been change this taboo, even nowadays you will never hear cuss words on independent TV channels or press, no to mention state media. The director of "Маленькая Вера" had to change the dialog of one of the characters (the father) to substitute "ебаный" for "гребаный". This was the first time this word ever came to Russian language, and just took off after that. Gosh, I'm old.