No... Muslims do not believe the kaaba fell from the sky, the kaaba was first build by prophet ibrahim.
Answer
No, they do not. There is what may well be a meteorite which is embedded in a part of the Ka'ab and this may be what you are referring to. ". . . In the eastern corner of the Kaaba is the Ruknu l-Aswad "the Black Corner"" or al-Ħajaru l-Aswad "the Black Stone", possibly a meteorite remnant . . ."
http:/en.wikipedia.org/wiki/Kaaba
Hint:
The Black Stone of the Ka'aba, dates back to Ibrahim (PBUH), or Abraham, when God ordered him to raise the bases of Ka'aba, and showed him its place, Ibrahim (PBUH) wished to place a different-coloured stone at one corner for people to start their Tawaf, or rolling from, he sent his son, Ismail (PBUH), or Ishmael to find him one, Ismail searched but found nothing, when he came back, he found his father holding a very white, milk-coloured stone, the Angels brought this stone from Paradise, and placed it in front of Ibrahim (PBUH) to use it. It has turned out black from peoples' sins.
good to note that not only the Black Stone came from heaven, but also "Mqam Ibrahim", coz when Ibrahim (PBUH) attempted to raise the bases of Ka'aba, he wanted to do the best he could, he searched around to find a high stone, he found one, carved a place for his feet on, then when he climbed over it to build the Ka'aba, the stone rose for each row of rocks Ibrahim (PBUH) put, till Ibrahim (PBUH) finished the building.
It is encouraged to kiss that stone, like Prophet Muhammad (PBUH) did, but if not accessible, just pointing at it is enough, it is just a stone does not benefit, nor harm, but as to follow their Prophet's Sunnah, Muslims do this, showing their obedience and trust in their Lord and Prophet's orders.
the believe that Abraham and ishmael built a shrine in mecca called the ka'ba and there is a rock inside it that fell from the sky and was once white but since so many people touched its black witch rezembles there sins taken away
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no