Translation is not working for Breadcrumbs injected via layout update file. Refer below XML code:

local.xml

<checkout_cart_index>
  <reference name="breadcrumbs">
		<action method="addCrumb">
			<crumbName>home</crumbName>
			<crumbInfo>
				<label>Home</label>
				<title>Home</title>
				<link>/</link>
			</crumbInfo>
		</action>
		<action method="addCrumb">
			<crumbName>cart</crumbName>
			<crumbInfo>
				<label>Cart</label>
				<title>Cart</title>
			</crumbInfo>
		</action>
	</reference>
</checkout_cart_index>