For a country that was used to decades of autarky, where most people spent their formative years in a FERA mindset, a key hurdle in re-integrating with the world economy is the incomprehensibility of capital flows. Many people are hostile to capital flows on the grounds that foreign capital is capricious and ignorant. If you can't understand it, it must be a fad :-)
One of the nice things that has been happening in India's deepening engagement with the world is a buildup of data about the international finance aspects of the economy. It is now possible to look at a good monthly time-series with 140 observations with data for net FII inflows. And, it's now possible to look at data for the thousands of firms in the CMIE database and ponder which of them have foreign shareholding and why.
I wrote an article Understanding the FII in Business Standard today which conveys an executive summary of what one finds from these two lines of thought.
The first few paragraphs (looking at the time-series characteristics of net FII inflows) is unpublished work. The results using firm-level data are on the website of the NIPFP-DEA Research Program on Capital Flows and their Consequences (slideshow, paper).