What does Bhakti Yoga say about the nature of God in the Bhagavad Gita?
The first poster seems to me to have it right. "God is love" is a repeated phrase that I've heard in bhakti yoga, with the god Krishna being one of the key names repeated in prayers and phrases. (Hanuman's unswerving devotion to Ram is also mentioned a lot, but that's from another set of writings.) As I understand the term, "yoga" is related to the English word "yoke," meaning to join the body and mind (and soul, if you will) to create a purposeful unity. Different branches (or limbs, as they're sometimes called) of yoga have different emphases, such as physical exercise, breath, meditation, or (in the case of bhakti yoga) the cultivation of love and devotion towards others in one's life. The wikipedia entry on "bhakti yoga" gives a brief overview, including a short secton on the Bhagavad Gita.
Bhagwad Gita has described several alternate ways or practices for achieving the ultimate happiness or deliverance from the cycle of birth and death. Each of this type of practice is named a different type of yoga. Bhakti yoga, which means practice based on devotion to the ultimate god, is one of these alternate practice. The details of Bhakti yoga are covered primarily in the twelfth chapter of Gita. However, this chapter describes the ways and characteristics of a devotee rather than the nature of god. Thus Gita describes no particular view of God applicable exclusively to Bhakti Yoga.
However, Gita does describe he nature of ultimate god at many different places in many different ways. The word limitation of eNoes, as well as complexity of the concepts, make it difficult for me to give a comprehensive description of nature of God as per Gita. However stated in very simple words God has two different broad characteristics, which are apparently mutually exclusive. Thus God is Described as formless (nirakar), At the same time, God also takes on form as a sakar incarnation.
The nirakar or formless God is something that has no matter, occupies no space, has no form or any other qualities - like colour, taste, mass and state - possessed by physical matters, has no beginning and no end. It is interesting to note that having no beginning and no end, makes the God of Geeta as something infinite, as well as nothing. Thus Gita says that when everything is eliminated, what remains is the God.
The sakar God refers to incarnation of god in human or some other form. The nirakar God takes on different sakar forms from time to time for renovation or re-establishment (sansthapanarthaya) of codes of good conduct (dharma), for protection (paritranaya) of the righteous people, and for elimination (vinashaya) of evil doers. Bhakti Yoga generally is based on devotion to such sakar God.
i'm not too sure about this but i think it says that if you love God, God wil love you too.