Short answer: no, since styles don't apply across document boundaries.
However, since you have an <object> tag you can insert the stylesheet into the svg document using script.
Something like this, and note that this code assumes that the <object> has loaded fully:
var svgDoc = yourObjectElement.contentDocument;
var styleElement = svgDoc.createElementNS("http://www.w3.org/2000/svg", "style");
styleElement.textContent = "svg { fill: #fff }"; // add whatever you need here
svgDoc.getElementById("where-to-insert").appendChild(styleElement);
It's also possible to insert a <link> element to reference an external stylesheet:
var svgDoc = yourObjectElement.contentDocument;
var linkElm = svgDoc.createElementNS("http://www.w3.org/1999/xhtml", "link");
linkElm.setAttribute("href", "my-style.css");
linkElm.setAttribute("type", "text/css");
linkElm.setAttribute("rel", "stylesheet");
svgDoc.getElementById("where-to-insert").appendChild(linkElm);
Yet another option is to use the first method, to insert a style element, and then add an @import rule, e.g styleElement.textContent = "@import url(my-style.css)".
Of course you can directly link to the stylesheet from the svg file too, without doing any scripting. Either of the following should work:
<?xml version="1.0" encoding="UTF-8"?>
<?xml-stylesheet href="my-style.css" type="text/css"?>
<svg xmlns="http://www.w3.org/2000/svg">
... rest of document here ...
</svg>
or:
<svg xmlns="http://www.w3.org/2000/svg">
<defs>
<link href="my-style.css" type="text/css" rel="stylesheet"
xmlns="http://www.w3.org/1999/xhtml"/>
</defs>
... rest of document here ...
</svg>
Update 2015: uyou can use jquery-svg plugin for apply js scripts and css styles to an embedded SVG.
