Here are your Apple rumors and AAPL news items for today:

Chip Rebuff: Taiwan Semiconductor Manufacturing Company (NYSE:TSM) has spurned Apple’s (NASDAQ:AAPL) bid to gain exclusive rights to its smartphone chips in exchange for a hefty cash investment in the company, Bloomberg reports. Apple offered to invest more than $1 billion in the chip maker if it would guarantee a certain amount of chips solely for its use. TSM declined the offer in order to maintain full control over its patents and technology. Apple was not alone in making such an offer. Qualcomm (NASDAQ:QCOM) also proposed a similar $1 billion investment in TSM. Apple is attempting to diversify its component supply chain. Currently, smartphone rival Samsung supplies the company with the main chips for the iPhone and iPad, a relationship that has become complicated by the two companies’ ongoing patent infringement battle.

Genius at Home: Purchasers of Apple’s iPhones and iPads in a number of countries now have the option of receiving the company’s Genius Bar technical support over the Internet, ZDNet notes. The online support option has been introduced in Germany, Spain, the U.K. and Brazil. Users can access the support by visiting the company’s online Apple Store and then clicking “Ask Now” to open an online dialog with technical support staff or initiate a telephone call. The service allows online buyers to ask questions about products before they buy them, or to get assistance with technical problems or setting up their devices once they arrive. Support is only available for iPads and iPhone, however. Technical support for Macs and iPods is not currently included in the service.

Trouble at the Top: With rumors of increasing employee discontent at Apple’s highly profitable outlet stores growing, many have blamed new retail chief John Browett, but a new report says the problem emanates from the CEO’s office instead, according to Fortune. The company was forced to admit a “mistake” regarding Apple Store staffing calculations this month, leading many to criticize Browett, who succeeded the customer-focused Ron Johnson, who left Apple to restructure faltering discount chain J.C. Penney (NYSE:JCP). However, sources say that Tim Cook has been the driving force behind changes at the Apple Stores, insisting on a focus on higher profits instead of customer satisfaction. In fact, sources say this happened three years ago when Cook exerted similar pressure on Johnson. At that time, however, Johnson had the late Steve Jobs’ backing and resisted Cook’s direction. Cook apparently hired Browett due to their agreement on the need to concentrate on sales.

For more about the company, check out our previous Apple Rumors stories.